Methods for the augmentation, exploration, and maintenance of project hierarchies

ABSTRACT

A method is provided for graphically representing a portion of a directed acyclic graph as a hierarchical tree structure to facilitate user collaboration over a network, the method comprising obtaining a collaborative project shared among a plurality of users over a communication network, the project represented by a directed acyclic graph structure comprising a plurality of entities and a plurality of associations, the plurality of entities including one or more locus entities, each of the locus entities associated with a locus node from which ancestor entities in the directed acyclic graph of each locus entity are traversed as an inverted tree structure, each child node in the inverted tree indicating a respective entity related as a parent in the directed acyclic graph to the entity of its parent in the inverted tree; and expanding a subtree rooted at a leaf node of the inverted tree in response to user input.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/260,072, filed Nov. 25, 2015 and entitled“Methods for the Augmentation, Exploration, and Maintenance of ProjectHierarchies,” which is hereby incorporated by reference herein.

BACKGROUND

This disclosure relates to the layout and augmentation of hierarchicalstructures representing project information, including projectsthemselves and related information; to exploration through hierarchicalstructures; and to maintenance of those structures when modified in acollaborative setting.

SUMMARY

In some embodiments, this disclosure provides a method, when augmentinga DAG (possibly a tree) that presents entities of at least two kinds andfor which one entity of the first (independent) kind may be directlyassociated with an entity of the second (dependent) kind, for extendingthis relation such that every entity of the second kind is indirectlyassociated with one entity of the first kind.

In some embodiments, this disclosure provides a method, when navigatinga DAG such that one or more locus nodes are central, for providingaccess to information that is neither strictly in the substructure ofthe locus nodes nor strictly in their context, but rather is inheritedinto the substructure via an association with the context. Moreover,top-down augmentation of such inherited structure implies refinement ofthat structure with respect to one or more locus nodes that inherit thatstructure, in a manner that we will define more precisely. It may alsobe appropriate to inherit information into the context via associationwith the substructure. Likewise, bottom-up augmentation of suchinherited structure implies refinement of that structure with respect toone or more locus nodes that inherit that structure. Alternatively,top-down augmentation of a node in the context may imply generalizationof the preceding context with respect to the relevant locus nodes.

Some embodiments described herein first represent a state of navigationof a DAG as either one or a pair of logical trees (one for substructureand another, inverted, for context), as is initially done for “A Methodfor Exploration of Hierarchical Structures and Representation of ContextThereof”, or using Venn diagrams or any other means, and then augmentsthe substructure with additional information inherited from the context(or vice versa). Upon augmentation of such inherited structure, thenative substructure is built out as necessary with refinements ofinherited structure, initially with respect to the locus nodes andcontinuing incrementally with respect to the recently added nativesubstructure. The process is similar for augmenting context withinformation inherited from the substructure.

This disclosure includes other related aspects of DAGs presentingproject information and their augmentation.

Furthermore, this disclosure provides a method, when navigating a DAG,for constraining a subDAG and its context so that they can be visualizedand focused on as a tree, such that any entity is only represented by asingle node in the visualization at any point in time. In someembodiments, we describe three operations: tree initialization, nodeexpansion, and node collapse. A preliminary process to treeinitialization, tree construction, is relevant for the Static LifetimeStrategy; the Dynamic Lifetime Strategy incorporates node constructioninto the initialization process. The latter two operations supportexploration of the hierarchy and may potentially apply to eithersubstructure nodes or context nodes. From the locus node or any visiblesubstructure node, e.g., we might expand or collapse to view or hide,respectively, deeper substructure, and from the locus node or anyvisible context node we might expand or collapse to view or hide,respectively, more lofty context. The disclosure also provides a methodfor regulating the set of locus nodes by selecting and deselecting facetvalues and revealing the common ancestors and descendants of the variouslocus nodes.

This disclosure, in a simplified exposition, first represents a state ofnavigation of a DAG as a pair of logical trees (for substructure andcontext) and then represents these in a substrate tree. Then, in a morecomplex exposition, it first represents a state of navigation of aDAG-forest as a sequence of pairs of logical trees (for substructure andcontext, with substructures potentially overlapping with substructuresand contexts potentially overlapping with contexts) and then representsthese in a substrate tree.

Some embodiments maintain the state of the frontier of expansion ofsubstructure or context, or both, so that a single user action appliedto substructure nodes (along with the locus node) can expand or collapsethat node's substructure, and a single user action applied to contextnodes (along with the locus node) can expand or collapse that node'scontext.

One key insight is that upon expanding substructure or context for anode, it is necessary to automatically collapse any potentiallyconflicting substructure or context, respectively. Another key insightis that substructure and context can be represented as a nested sequenceof lists of two varieties to facilitate visualization of commondescendants and ancestors, respectively, as will be described herein.

References to parents and children of entities refer to the underlyingDAG. References to parents and children that specifically mentionsubstructure or context generally refer to the corresponding logicaltree. References to parents and children of nodes otherwise refer to anabstracted substrate tree and must be adapted to apply to HTML or anyother particular substrate tree.

Additionally, some embodiments maintain system history by arrangingchange records in a DAG, not by explicit branching and mergingdirectives, but by branching and merging on the basis of the contentthat is affected by each change, so that distinct content is modified inseparate branches while the same content must be modified sequentially.

Some embodiments may also maintain the visibility of system data suchthat different views of the global DAG are provided depending on therole of a user with respect to a project (or related project in thehierarchy) or the user's prior history in creating or modifying theentities involved. The configuration of system data is dependent uponrelationships that may be formed between users.

In various embodiments, a method is presented for allowing a user tosafely and efficiently jointly specialize one or more nodes in a DAG,each of which shares a common ancestor with a locus node, whileassociating the new refining node with a locus node, by presenting thenodes to be refined as inherited descendants of the locus node; a methodfor allowing a user to safely and efficiently jointly generalize one ormore nodes in a DAG, each of which shares a common ancestor with a node,while associating the new refined node with the common ancestor, bytreating the refining nodes as locus nodes and initiating the operationfrom the common ancestor.

In various embodiments, a method is presented for allowing a user toexplore a hierarchical structure in the form of a directed acyclic graphsuch that one or more nodes are distinguished as loci. Descendants oflocus nodes can be explored as a tree and ancestors of locus nodes canbe explored as an inverted tree. As some nodes are expanded, others arecollapsed such that any entity is only represented by a single visiblenode. Where the same entity is reached through the ancestors ordescendants of multiple locus nodes, that entity is represented by asingle node.

In various embodiments, a method is presented for allowing various usersto coordinate their access to and modifications of project structurethat allows rollbacks via a hierarchy-based user interface of sequentialchanges to particular independently generated content without disturbingother content and supports intuitive merging of conflicting changes.

Various embodiments provide systems, methods, and non-transitorycomputer readable medium for graphically representing a portion of adirected acyclic graph as a hierarchical tree structure to facilitateuser collaboration over a communication network. The systems, methods,and computer readable medium may be configured to perform obtaining acollaborative project shared among a plurality of users over acommunication network, the collaborative project represented by adirected acyclic graph structure comprising a plurality of entities anda plurality of associations, the plurality of entities including one ormore locus entities, each of the one or more locus entities associatedwith a locus node from which descendant entities, in the directedacyclic graph, of each locus entity are traversed as a tree structure,each child node in the tree indicating a respective entity related as achild in the directed acyclic graph to the entity of its parent in thetree; and expanding a subtree rooted at a leaf node of the tree inresponse to user input.

Various embodiments provide systems, methods, and non-transitorycomputer readable medium for graphically representing a portion of adirected acyclic graph as a hierarchical tree structure to facilitateuser collaboration over a communication network. The systems, methods,and computer readable medium may be configured to perform obtaining acollaborative project shared among a plurality of users over acommunication network, the collaborative project represented by adirected acyclic graph structure comprising a plurality of entities anda plurality of associations, the plurality of entities including one ormore locus entities, each of the one or more locus entities associatedwith a locus node from which ancestor entities in the directed acyclicgraph of each locus entity are traversed as an inverted tree structure,each child node in the inverted tree indicating a respective entityrelated as a parent in the directed acyclic graph to the entity of itsparent in the inverted tree; and expanding a subtree rooted at a leafnode of the inverted tree in response to user input.

In some embodiments, the systems, methods, and non-transitory computerreadable medium are configured to collapse the subtrees rooted at leastone other node of the tree in response to the expanding the at least onenode of the plurality of nodes in response to the user input, therebyallowing a particular entity of the plurality of entities to begraphically represented by a single visible node of the plurality ofnodes.

In some embodiments, the systems, methods, and non-transitory computerreadable medium are configured to collapse the subtrees rooted at leastone other node of the inverted tree in response to the expanding the atleast one node of the plurality of nodes in response to the user input,thereby allowing a particular entity of the plurality of entities to begraphically represented by at most a single visible node of theplurality of nodes.

In some embodiments, some entities are associated with any of one ormore files, one or more progress reports each covering a time period,one or more records of contributions to the project, related entitiesthat can be set as locus nodes whose substructure can be explored by auser, or other auxiliary data; and the systems, methods, andnon-transitory computer readable medium are configured to display anaggregation of any of the one or more files, progress reports eachcovering a time period, one or more records of contributions to theproject, or any other auxiliary data associated with the particularentities indicated by each visible node.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and where at least one proper refinement ancestor ofone or more of the locus entities is further associated with one or moreother descendants that are not descendants of the corresponding one ormore locus entities, and the one or more other descendants arerepresented distinctly as inherited descendants of the corresponding oneor more locus nodes indicating the respective one or more locusentities.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to cause an augmentation of the directedacyclic graph by a first operation, the first operation adding a newnode to the plurality of nodes, the first operation initiated from aparticular node of the plurality of nodes, the new node appearing as achild of the particular node; and creating a new entity associated withthe new node and an association between the new entity and theparticular entity, the kinds of the new node and association based onthe first operation.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to perform, upon initiation by a userfrom an initiating inherited node from among the plurality of nodes,connected to a locus node by a path comprised of inherited nodes, of arestatement operation or of a second operation to be performed upon thefinal restating node of the path and as a precursor to that secondoperation, for each inherited node on the path from the locus node,exclusive of the locus node: creating a restating entity; creating afirst association between the restating entity and the entity indicatedby the locus node, wherein the first association being of the same kindas the association between the inherited entity and the properrefinement ancestor, if the locus node is the parent of the inheritednode, or between the restating entity and the result of restating theparent of the inherited node along the path, wherein the firstassociation being of the same kind as the association between the entityindicated by the inherited node and the entity indicated by its parentnode, if the locus node is not the parent of the inherited node; andcreating a second association between the restating entity and theinherited entity being restated, wherein the restating entity refinesthe inherited entity being restated.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to perform, upon initiation by a userfrom an initiating inherited node from among the plurality of nodes,connected to a locus node by a path comprised of inherited andnoninherited nodes, of a restatement operation or of a second operationto be performed upon the final restating node of the path and as aprecursor to that second operation, for each node on the path from thelocus node, exclusive of the locus node: creating a restating entity ifthe path node was inherited; creating a first association, if the parentof the path node was inherited or is the locus node, between therestating entity if the path node was inherited or else the path nodeand either the entity indicated by the locus node, wherein the firstassociation being of the same kind as the association between the pathentity and the proper refinement ancestor, if the locus node is theparent of the path node or the result of restating the parent of thepath node along the path, wherein the first association being of thesame kind as the association between the entity indicated by the pathnode and the entity indicated by its parent node, if the locus node isnot the parent of the path node; and creating a second association, ifthe path node was inherited, between the restating entity and theinherited path entity being restated wherein the restating entityrefines the inherited path entity being restated.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to perform, upon initiation by a userfrom a plurality of inherited initiating nodes from among the pluralityof nodes, each inherited initiating node connected to a locus node by acorresponding path comprised of inherited nodes of a restatementoperation or of a second operation to be performed upon the finalrestating nodes of each path and as a precursor to that secondoperation, for each node on any path from among the plurality of paths,exclusive of the locus node: creating a restating entity; creating afirst association between the restating entity and the entity indicatedby the locus node, wherein the first association being of the same kindas the association between the inherited entity and the properrefinement ancestor, if the locus node is the parent of the inheritednode, or between the restating entity and the result of restating theparent of the inherited node along the corresponding path, wherein thefirst association being of the same kind as the association between theentity indicated by the inherited node and the entity indicated by itsparent node, if the locus node is not the parent of the inherited node;and creating a second association between the restating entity and theinherited entity being restated wherein the restating entity refines theinherited entity being restated.

In some embodiments, the at least one other child may be associated withone or more descendants that are not descendants of the locus node, andthe one or more descendants are represented distinctly as inheriteddescendants of the locus node; and the at least one other child isassociated with one or more descendants that are not descendants of thelocus node, and the descendants may include a restating refinement; andthe restating node and its descendants may be excluded from theinherited descendants of the locus node.

In some embodiments, the at least one other child is associated with oneor more descendants that are not descendants of the locus node, and theone or more descendants may be represented distinctly as inheriteddescendants of the locus node; and the at least one other child may berestated by a descendant of the locus node; and the other child may beexcluded from the inherited descendants of the locus node.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to cause an augmentation of the directedacyclic graph by a first operation, the first operation adding a newnode to the plurality of nodes, the first operation initiated from aparticular node of the plurality of nodes, the new node appearing as achild within the inverted tree of the particular node; and creating anew entity associated with the new node and an association between thenew entity and the particular entity, the kind of the new node being thesame as the kind of the particular node and the kind of the associationbeing refinement, with the particular node refining the new node.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to perform upon initiation of anoperation by a user from an initiating context node from among theplurality of nodes, for each of a plurality of context nodes on the pathbetween the initiating context node and the corresponding locus node,exclusive of the initiating context node: creating a generalizingentity, the kind of the new entity being the same as the kind of thecontext node; creating a first association between the generalizingentity and the entity indicated by the initiating context node, whereinthe first association being of the same kind as the association betweenthe context entity and the entity indicated by the initiating contextnode, if the context node is the parent within the inverted tree of theinitiating context node, wherein the first association being of the samekind as the association between the entity indicated by the context nodeand the entity indicated by its child node within the inverted tree, ifthe context node is not the parent within the inverted tree of theinitiating context node; and creating a second association between thegeneralizing entity and the entity indicated by the context node whereinthe generalizing entity is refined by the entity indicated by thecontext node.

In some embodiments, the inverted tree structures are formed within aforest structure comprising a plurality of tree structures, such thateach tree structure comprises two lists presented in a substrate tree bynesting one within the other: a first list of tree structures a secondlist of nodes, wherein: all nodes in any second list except the lastnode have no children in the substrate tree; locus nodes have nosiblings or children in the substrate tree; the entities indicated byeach node in any second list are parents in the directed acyclic graphof the first child in the substrate tree's second list of each child inthe substrate tree's first list of the last node in the second list.

In some embodiments, the tree structures are formed within a foreststructure comprising a plurality of tree structures, such that each treestructure comprises two lists presented in a substrate tree by nestingone within the other: a first list of tree structures including adesignated node a second list of nodes, wherein: each entity indicatedby a node in any second list has no children and is a child in thedirected acyclic graph of the entity indicated by the designated node oftheir parent tree structure in the substrate tree the outermost treestructures have lists of only locus nodes; the entity indicated by thedesignated node of each tree structure in any first list are children inthe directed acyclic graph of the entity indicated by the designatednode of the parent of their parent in the substrate tree.

In some embodiments, entities are each of a particular kind andassociations are each of a particular kind, one such kind of associationbeing refinement; and the systems, methods, and non-transitory computerreadable medium are configured to perform upon initiation of anoperation by a user from an initiating context node from among theplurality of nodes, for each of a plurality of context nodes on any paththrough the substrate tree between the initiating context node and alocus node, exclusive of the initiating context node, comprising thefirst element of each first list other than that including theinitiating context node: creating a generalizing entity; creating afirst association between the generalizing entity and the entityindicated by the initiating context node, wherein the first associationbeing of the same kind as the association between the context entity andthe entity indicated by the initiating context node if the context nodeis the parent within the inverted tree of the initiating context node,wherein the first association being of the same kind as the associationbetween the entity indicated by the context node and the entityindicated by its child node within the inverted tree, if the contextnode is not the parent within the inverted tree of the initiatingcontext node; and creating a second association between the generalizingentity and the entity indicated by the context node wherein thegeneralizing entity is refined by the entity indicated by the contextnode.

In some embodiments, the created generalizing refinements compriserestatements.

Various embodiments provide systems, methods, and non-transitorycomputer readable medium for graphically representing a portion of adirected acyclic graph as a hierarchical tree structure to facilitateuser collaboration over a communication network. The systems, methods,and non-transitory computer readable medium may be configured to performobtaining a collaborative project shared among a plurality of users overa communication network, the collaborative project represented by adirected acyclic graph structure comprising a plurality of entities eachof a particular kind and a plurality of associations, each of aparticular kind, one such kind being refinement, the plurality ofentities including at least one locus entity, each of the at least onelocus entity is associated with a locus node from which descendantentities, in the directed acyclic graph, of each locus entity aretraversed as a tree structure, each child node in the tree indicating arespective entity related as a child in the directed acyclic graph tothe entity of its parent in the tree, such that where at least oneproper refinement ancestor of one or more of the locus entities isfurther associated with one or more other descendants that are notdescendants of the corresponding one or more locus entities, and each ofthe at least one other descendants is represented distinctly as aninherited descendant of the corresponding at least one locus nodeindicating the at least one locus entity; and expanding a subtree rootedat a leaf node of the tree in response to user input.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

Arrows in data flow diagrams indicate a flow of information from theprocessing unit at the tail to the processing unit at the head. The dataflow diagrams use a double arrow head to indicate that an inflow maycause a change in the state of a component and a single arrow headotherwise.

Process flow diagrams make use various directives in ovals includingSTART, STOP, CONTINUE, and FAIL directives. Statement blocks appear asrectangles and decision points appear as diamonds. Iteration over a datastructure is indicated by a “for” block, which appears as a largerectangle containing instructions to be executed for each iteration.

Arrows in process flow diagrams indicate a flow of control from theprocessing unit at the tail to the processing unit at the head. If aline meets a processing unit at an arrow head, control flows to thatprocessing unit, otherwise it flows away from the processing unit. Whenmultiple lines leave a processing unit, all paths are to be taken in anyorder, or simultaneously, with proper attention to any shared resourcesas is familiar to those skilled in the art of software development. Anexception may be a fork from a diamond-shaped node, at which all pathssucceeding in their specified condition are to be taken in any order, orsimultaneously, with the same caveat. The above conventions are only forpurposes of presenting intuition about the relationships between variousprocessing steps, and not to provide an exhaustive exposition of all ofthe processing steps or all possible orderings of such steps throughwhich embodiments might be realized.

The process flow diagrams may make use of arrows to clusters of steps toindicate subroutine calls on component data, including recursivesubroutine calls. If additional work remains to be done after arecursive call, the execution of such remaining work may be indicatedexplicitly by a CONTINUE directive or implicitly with a STOP directive.This recursion is an expository mechanism. The underlying computationmay be implemented using recursion, iteration, macro expansion, and thelike.

An arc from the inside of a processing unit to the outside can beinterpreted as any other arrow, although such arrows are candidates forimplementation via recursive calls. To aid intuition, we informally usethe language of recursion to describe such arrows in the textdescriptions, although embodiments may or may not choose to implementthem as such. When descriptions refer to a stack, it is often the casethat the system stack assumed by most programming languages willsuffice.

Disjunction symbols (V) at branches indicate that exactly one pathshould be taken. Conjunction symbols (A) at branches indicate that allpaths are taken independently, with no constraints on the respectiveflow of the branches other than those imposed by shared resources atlower levels of implementation. We intend that all such computationsmeet at join points before one proceeds.

Arrows in block structure diagrams indicate that the module at the headis implemented using the module at the tail.

Drawing elements occurring in more than one place but assigned the samecode are assumed to refer to the same thing in the presented embodiment,although other embodiments may distinguish them.

FIG. 1 is an initial user screen according to some embodiments.

FIG. 2 is a user screen after clicking on “Create a new challenge”according to some embodiments.

FIG. 3 is a user screen after typing an initial problem name accordingto some embodiments.

FIG. 4 is a user screen after action creating an initial problemaccording to some embodiments.

FIG. 5 is a project screen selecting the specializing action on a rootproblem according to some embodiments.

FIG. 6 is a project screen after typing a refining problem name.

FIG. 7 is a project screen selecting the solving action on a rootproblem according to some embodiments.

FIG. 8 is a project screen after typing a solution name according tosome embodiments.

FIG. 9 is a project screen after action to solve a root problemaccording to some embodiments.

FIG. 10 is a project screen selecting the componentizing action on asolution according to some embodiments.

FIG. 11 is a project screen after typing a component problem nameaccording to some embodiments.

FIG. 12 is a project screen showing inheritance of projects by arefining problem according to some embodiments.

FIG. 13 is a project screen showing inheritance of a project by arefining solution according to some embodiments.

FIG. 14 is a project screen selecting the specializing action on twoproblems according to some embodiments.

FIG. 15 is a project screen selecting the specializing action on aninherited project according to some embodiments.

FIG. 16 is a project screen restating an inherited solution in-placeaccording to some embodiments.

FIG. 17 is a project screen restating an inherited problem in-placeaccording to some embodiments.

FIG. 18 is a project screen refining a restated problem according tosome embodiments.

FIG. 19 is a project screen after restating of inherited projectsaccording to some embodiments.

FIG. 20 is a project screen showing parents of projects resulting fromrestating inherited projects according to some embodiments.

FIG. 21 is the ancestor project screen showing restated projects andtheir restatements according to some embodiments.

FIG. 22 is a top-level data flow diagram of an embodiment.

FIG. 23 is an interaction sequence diagram of several use cases of anembodiment.

In example DAGs and trees, for concreteness we assume that circlesrepresent problems and squares represent solutions, and collectivelynumber these sequentially. We do not indicate the kinds of association,since this is evident for this embodiment from the kinds of the sourceand the target of the association. Selected nodes are shown with aborder, and nodes from which an operation is initiated are shown with aborder and four evenly spaced notches.

FIG. 24 is a diagram displaying an example DAG representing a problemand solution space according to some embodiments.

FIG. 25 is a diagram displaying a subDAG of the example DAG from FIG. 24with navigation centered on one node (1), according to some embodiments.

FIG. 26 is a diagram displaying the subDAG of the example DAG centeredon one node (1) from FIG. 25 with navigation and some structure(including nodes 9, 11, 12, and 15) inherited, according to someembodiments. The link from node 10 to node 1 has been spliced out.

FIG. 27 is a diagram displaying the subDAG of the example DAG from FIG.26, presented as a tree exploring nodes 4 and 10, according to someembodiments.

FIG. 28 is a diagram displaying the exploration from FIG. 27 withnavigation centered on one node (1) during the process of explicitlyrefining solution nodes from the substructure (4 and 10) with a newsolution node (13), while presented as a tree, according to someembodiments.

FIG. 29 is a diagram displaying the example DAG after explicitrefinement of solution nodes 4 and 10 with new solution node 13 as shownin FIG. 28, according to some embodiments.

FIG. 30 is a diagram displaying the exploration from FIG. 27 withnavigation centered on one node (1) during the process of explicitlyrefining a solution nodes from the substructure (4) and an inheritedsolution node (10) with a new solution node (16) that solves problemnode 5, while presented as a tree, according to some embodiments.

FIG. 31 is a diagram displaying the example DAG after explicitrefinement of solution nodes 4 and 10 with new solution node 16 thatsolves problem node 5 as shown in FIG. 28, according to someembodiments.

FIG. 32 is a diagram displaying a subDAG of the example DAG from FIG. 24with navigation centered on one node (5), according to some embodiments.

FIG. 33 is a diagram displaying the subDAG of the example DAG withnavigation centered on one node (5) from FIG. 32 and some structure(including nodes 4, 7, 8, 9, 10, 11, 12, and 15) inherited, according tosome embodiments.

FIG. 34 is a diagram displaying the subDAG of the example DAG from FIG.33, presented as a tree exploring nodes 4 and 8, according to someembodiments.

FIG. 35 is a diagram displaying the exploration from FIG. 34 withnavigation centered on one node (5) during the process of solving thatproblem node and refining two inherited solution nodes (4 and 8) with anew solution node (14), while presented as a tree, according to someembodiments.

FIG. 36 is a diagram displaying the example DAG after solving problemnode 5 and refining solution nodes 4 and 8 with new solution node 14 asshown in FIG. 35, according to some embodiments.

FIG. 37 is a diagram displaying the subDAG of the example DAG from FIG.26, presented as a tree exploring nodes 12 and 15, according to someembodiments.

FIG. 38 is a diagram displaying the exploration from FIG. 37 withnavigation centered on one node (1) during the iterated process ofrefining two inherited solution nodes (12 and 15) with a new solutionnode (17), while presented as a tree, according to some embodiments.

FIG. 39 is a diagram displaying the example DAG after refining problemnodes 12 and 15 with new solution node 17 as shown in FIG. 38, accordingto some embodiments.

FIG. 40 is a diagram displaying the exploration from FIG. 37 withnavigation centered on one node (1) during the in-place, iteratedprocess of refining two inherited solution nodes (12 and 15) with a newsolution node (17), while presented as a tree, according to someembodiments.

FIG. 41 is a diagram displaying the exploration from FIG. 37 withnavigation centered on one node (1) after the in-place, iterated processof refining two inherited solution nodes (12 and 15) with a new solutionnode (17), according to some embodiments.

FIG. 42 is a block structure diagram of an embodiment for specializationwithout inheritance.

FIG. 43 is a process flow diagram of an embodiment of the DAG reductionprocess, according to some embodiments.

FIG. 44 is a process flow diagram of an embodiment of the redundantrefinement elimination process, according to some embodiments.

FIG. 45 is a process flow diagram of client action to perform a singlespecializing augmentation of a DAG without inheritance, according tosome embodiments.

FIG. 46 is a process flow diagram of the calculation of the greatestlower bound of objects of refined nodes with respect to the substructureand context trees without inheritance, according to some embodiments.

FIG. 47 is a process flow diagram of the calculation of the greatestlower bound of nodes with respect to both context and substructuretrees, according to some embodiments.

FIG. 48 is a process flow diagram of the calculation of the least upperbound of nodes with respect to a tree (context or substructure),according to some embodiments.

FIG. 49 is a process flow diagram of the calculation of the greatestlower bound of nodes with respect to a tree (context or substructure),according to some embodiments.

FIG. 50 is a process flow diagram of client action to generate a proofthat a specializing augmentation of a DAG reduced to substructure andcontext trees without inheritance and with indirect objects satisfiesconstraints, according to some embodiments.

FIG. 51 is a process flow diagram of server action to validate a proofthat a specializing augmentation of a DAG with indirect objectssatisfies constraints, according to some embodiments.

FIG. 52 is a process flow diagram of client action to generate a proofthat a specializing augmentation of a DAG reduced to substructure andcontext trees without inheritance and with only direct objects satisfiesconstraints, according to some embodiments.

FIG. 53 is a process flow diagram of server action to validate a proofthat a specializing augmentation of a DAG with only direct objectssatisfies constraints, according to some embodiments.

FIG. 54 is a diagram displaying an example DAG with navigation centeredon node 51, according to some embodiments.

FIG. 55 is a diagram displaying the example DAG from FIG. 54 aftersolving problem node 52 and refining solution node 54 with new solutionnode 55, according to some embodiments.

FIG. 56 is a process flow diagram of client action to perform a singlecross-kind and specializing augmentation of a DAG without inheritance,according to some embodiments.

FIG. 57 is a process flow diagram of client action to generate a proofthat a cross-kind and specializing augmentation of a DAG reduced tosubstructure and context trees without inheritance and with only directobjects satisfies constraints, according to some embodiments.

FIG. 58 is a process flow diagram of client action to generate a proofthat a cross-kind and specializing augmentation of a DAG reduced tosubstructure and context trees without inheritance and with indirectobjects satisfies constraints, according to some embodiments.

FIG. 59 is a process flow diagram of client action to generate a portionof a proof that an augmentation of a DAG reduced to substructure andcontext trees satisfies constraints, according to some embodiments.

FIG. 60 is a process flow diagram of server action to validate a proofthat a cross-kind and specializing augmentation of a DAG with indirectobjects satisfies constraints, according to some embodiments.

FIG. 61 is a process flow diagram of server action to validate a proofthat a cross-kind and specializing augmentation of a DAG with onlydirect objects satisfies constraints, according to some embodiments.

FIG. 62 is a block structure diagram of an embodiment forspecialization.

FIG. 63 is a process flow diagram of an embodiment of the DAGlocalization process, according to some embodiments.

FIG. 64 is a process flow diagram of an embodiment of the inheritanceprocess, according to some embodiments.

FIG. 65 is a process flow diagram of an indeterminate embodiment of thecomponent of the inheritance process that collects structure to beinherited, according to some embodiments.

FIG. 66 is a process flow diagram of the component of an embodiment ofthe inheritance process that connects inherited structure to the DAG,according to some embodiments.

FIG. 67 is a process flow diagram of the component of a shallowest-firstembodiment of the component of the inheritance process that collectsstructure to be inherited via preorder traversal, according to someembodiments.

FIG. 68 is a process flow diagram of the component of a deepest-firstembodiment of the component of the inheritance process that collectsstructure to be inherited via preorder traversal, according to someembodiments.

FIG. 69 is a process flow diagram of the component of an alternativedeepest-first embodiment of the component of the inheritance processthat collects structure to be inherited via postorder traversal,according to some embodiments.

FIG. 70 is a process flow diagram of the component of a deepest-firstembodiment of the inheritance process that connects inherited structureto the DAG, according to some embodiments.

FIG. 71 is a process flow diagram of the component of a deepest-firstembodiment of the component of the inheritance process that collectsstructure to be inherited and the path by which it is inherited,according to some embodiments.

FIG. 72 is a process flow diagram of the component of a deepest-firstembodiment of the component of the inheritance process that collectsstructure to be inherited and the flow (DAG) by which it is inherited,according to some embodiments.

FIG. 73 is a process flow diagram of client action to perform a singlespecializing augmentation of a DAG, according to some embodiments.

FIG. 74 is a process flow diagram of client action to generate a proofthat a specializing augmentation of a DAG reduced to substructure andcontext trees with inheritance and with indirect objects satisfiesconstraints, according to some embodiments.

FIG. 75 is a process flow diagram of client action to generate a proofthat a specializing augmentation of a DAG reduced to substructure andcontext trees with inheritance and with only direct objects satisfiesconstraints, according to some embodiments.

FIG. 76 is a process flow diagram of client action to generate anindependent node path of a proof that a specializing augmentation of aDAG reduced to substructure and context trees with inheritance satisfiesconstraints, according to some embodiments.

FIG. 77 is a process flow diagram of client action to perform a singlecross-kind and specializing augmentation of a DAG, according to someembodiments.

FIG. 78 is a process flow diagram of client action to generate a proofthat a cross-kind and specializing augmentation of a DAG reduced tosubstructure and context trees with inheritance and with indirectobjects satisfies constraints, according to some embodiments.

FIG. 79 is a process flow diagram of client action to generate a proofthat a cross-kind and specializing augmentation of a DAG reduced tosubstructure and context trees with inheritance and with only directobjects satisfies constraints, according to some embodiments.

FIG. 80 is a process flow diagram of client action to performspecializing augmentation of a DAG, according to some embodiments.

FIG. 81 is a process flow diagram of an alternative version of clientaction to perform specializing augmentation of a DAG that treatsrefinement of a single inherited node as part of the process of copyingrefined ancestors, according to some embodiments.

FIG. 82 is a process flow diagram of client action to perform cross-kindand specializing augmentation of a DAG, according to some embodiments.

FIG. 83 is a process flow diagram of client action to copy the inheritedancestors of a node, specialized to the locus node, according to someembodiments.

FIG. 84 is a trace diagram of an embodiment of the augmentation processfor the case of FIG. 38, according to some embodiments.

FIG. 85 is a trace diagram of an embodiment of the augmentation processmodified to handleAugment Inheritance Process Trace for NoncontiguousExample.

FIG. 86 is a process flow diagram of the component of a shallowest-firstembodiment of the component of the inheritance process that collectsstructure to be inherited and the path by which it is inherited, viarestatements, according to some embodiments.

FIG. 87 is a process flow diagram of the component of an embodiment ofthe inheritance process that connects inherited structure to the DAGwhile skipping unrelated restatements, according to some embodiments.

FIG. 88 is a process flow diagram of the component of an embodiment ofthe inheritance process that connects an inherited restatement to theDAG while skipping unrelated restatements, according to someembodiments.

FIG. 89 is a process flow diagram of client action to performspecializing augmentation that refines even a single inherited nodeafter restating it, according to some embodiments.

FIG. 90 is a process flow diagram of client action to restate theinherited ancestors of a node in place, specialized to the locus node,according to some embodiments.

FIG. 91 is a process flow diagram of client action to perform a singlespecializing restating augmentation of a DAG, according to someembodiments.

FIG. 92 is a process flow diagram of client action to perform a singlecross-kind and specializing restating augmentation of a DAG, accordingto some embodiments.

FIG. 93 is a diagram displaying a second example DAG according to someembodiments.

FIG. 94 is a diagram displaying a subDAG of the example DAG from FIG. 93with navigation centered on two nodes (22 and 23), according to someembodiments.

FIG. 95 is a diagram displaying the subDAG of the example DAG centeredon two nodes (22 and 23) from FIG. 94 with some structure (includingnodes 24 and 25) inherited, according to some embodiments.

FIG. 96 is a diagram displaying the subDAG of the example DAG from FIG.95, presented as a tree exploring nodes 24 and 25, according to someembodiments.

FIG. 97 is a diagram displaying the exploration from FIG. 96 withnavigation centered on two nodes (22 and 23) during the process ofsolving those problem nodes and refining two inherited solution nodes(24 and 25) with a new solution node (26), while presented as a tree,according to some embodiments.

FIG. 98 is a diagram displaying the example DAG from FIG. 93 aftersolving problem nodes 22 and 23 and refining solution nodes 24 and 25with new solution node 26 as shown in FIG. 97, according to someembodiments.

FIG. 99 is a diagram displaying a third example DAG with navigationcentered on node 31, according to some embodiments.

FIG. 100 is a diagram displaying the example DAG from FIG. 99, presentedas a substructure tree exploring nodes 36 and 37, according to someembodiments.

FIG. 101 is a diagram displaying the exploration from FIG. 100 withnavigation centered on node 31 during the process of generalizing twodependent nodes (36 and 37) with a new dependent node (38), whilepresented as a tree, according to some embodiments.

FIG. 102 is a diagram displaying the example DAG from FIG. 99 afteraugmenting independent node 31 and generalizing dependent nodes 36 and37 with new dependent node 38 as shown in FIG. 101, according to someembodiments.

FIG. 103 is a diagram displaying a fourth example DAG with navigationcentered on nodes 46 and 47, according to some embodiments.

FIG. 104 is a diagram displaying the example DAG from FIG. 103,presented as a pair of overlapping context trees exploring node 41,according to some embodiments.

FIG. 105 is a diagram displaying the exploration from FIG. 104 withnavigation centered on nodes 46 and 47 during the process of augmentingnode 41 while generalizing two dependent nodes (48 and 49) with a newdependent node (50), while presented as a tree, according to someembodiments.

FIG. 106 is a diagram displaying the example DAG from FIG. 103 afteraugmenting independent node 41 and generalizing dependent nodes 48 and49 with new dependent node 50 as shown in FIG. 105, according to someembodiments.

FIG. 107 is a diagram displaying a fifth example DAG with navigationcentered on nodes 74 and 75, according to some embodiments.

FIG. 108 is a diagram displaying the example DAG from FIG. 107 aftersolving problem nodes 70 with new solution node 78 that generalizes theexisting solution nodes and is componentized by generalizations of theexisting solution components, according to some embodiments.

FIG. 109 is a block structure diagram of an embodiment forgeneralization without inheritance.

FIG. 110 is a process flow diagram of client action to perform a singlegeneralizing augmentation of a DAG, according to some embodiments.

FIG. 111 is a process flow diagram of the calculation of the least upperbound of objects of refining nodes with respect to the substructure andcontext trees without inheritance, according to some embodiments.

FIG. 112 is a process flow diagram of the calculation of the least upperbound of nodes with respect to both context and substructure trees,according to some embodiments.

FIG. 113 is a project screen selecting a solution to open forgeneralization, according to some embodiments.

FIG. 114 is a project screen selecting a second solution to open forgeneralization, according to some embodiments.

FIG. 115 is a project screen selecting generalizing solution operation,according to some embodiments.

FIG. 116 is a project screen solving a problem while abstractingsolutions, according to some embodiments.

FIG. 117 is a project screen refining that solution while abstractingothers, according to some embodiments.

FIG. 118 is a project screen after iterated abstracting solution,according to some embodiments.

FIG. 119 is a project screen from alternate specialized problem afteriterated abstracting solution, according to some embodiments.

FIG. 120 is a project screen selecting generalization to restatementoperation, according to some embodiments.

FIG. 121 is a project screen entering specialization of new generalizedsolution, according to some embodiments.

FIG. 122 is a process flow diagram of client action to generate a proofthat a generalizing augmentation of a DAG reduced to substructure andcontext trees without inheritance and with indirect objects satisfiesconstraints, according to some embodiments.

FIG. 123 is a process flow diagram of server action to validate a proofthat a generalizing augmentation of a DAG with indirect objectssatisfies constraints, according to some embodiments.

FIG. 124 is a process flow diagram of server action to validate a proofthat a generalizing augmentation of a DAG with only direct objectssatisfies constraints, according to some embodiments.

FIG. 125 is a process flow diagram of client action to perform a singlecross-kind and generalizing augmentation of a DAG, according to someembodiments.

FIG. 126 is a process flow diagram of client action to generate a proofthat a cross-kind and generalizing augmentation of a DAG reduced tosubstructure and context trees without inheritance and with indirectobjects satisfies constraints, according to some embodiments.

FIG. 127 is a process flow diagram of client action to generate a proofthat a cross-kind and generalizing augmentation of a DAG reduced tosubstructure and context trees without inheritance and with only directobjects satisfies constraints, according to some embodiments.

FIG. 128 is a process flow diagram of server action to validate a proofthat a cross-kind and generalizing augmentation of a DAG with indirectobjects satisfies constraints, according to some embodiments.

FIG. 129 is a process flow diagram of server action to validate a proofthat a cross-kind and generalizing augmentation of a DAG with onlydirect objects satisfies constraints.

FIG. 130 is a block structure diagram of an embodiment for iteratedgeneralization.

FIG. 131 is a process flow diagram of client action to performcross-kind and generalizing augmentation of a DAG, according to someembodiments.

FIG. 132 is a diagram displaying an example DAG with navigation centeredon node 61 or 64 and 66, according to some embodiments.

FIG. 133 is a diagram displaying the example DAG from FIG. 132 aftercreating a refinement association from existing node 66 to existing node64, according to some embodiments.

FIG. 134 is a process flow diagram of client action to performaugmentation of a DAG with a refinement association between nodes in thesubstructure, according to some embodiments.

FIG. 135 is a process flow diagram of client action to performaugmentation of a DAG with a refinement association between locus nodes,according to some embodiments.

FIG. 136 is a process flow diagram of client action to perform a singleaugmentation of a DAG by adding a refinement association betweenexisting entities, according to some embodiments.

FIG. 137 is an initial global example DAG for describing therepresentation of conditions in data measure problems, according to someembodiments.

FIG. 138 is a local condition DAG for the example of FIG. 137 innavigation at node 80, according to some embodiments.

FIG. 139 is a local condition DAG for the example of FIG. 137 innavigation at node 81, before application of Specialize Terms, accordingto some embodiments.

FIG. 140 is a local condition DAG for the example of FIG. 137 innavigation at node 81, after application of Specialize Terms (and lateroperations), according to some embodiments.

FIG. 141 is a local condition DAG for the example of FIG. 137 innavigation at node 82, before application of Remove Disjunct, accordingto some embodiments.

FIG. 142 is a local condition DAG for the example of FIG. 137 innavigation at node 82, after application of Remove Disjunct (and lateroperations), according to some embodiments.

FIG. 143 is a local condition DAG for the example of FIG. 137 innavigation at node 83, before application of Add Conjunct, according tosome embodiments.

FIG. 144 is a local condition DAG for the example of FIG. 137 innavigation at node 83, after application of Add Conjunct (and lateroperations), according to some embodiments.

FIG. 145 is a local condition DAG for the example of FIG. 137 innavigation at node 84, before application of Merge Disjuncts, accordingto some embodiments.

FIG. 146 is the final global DAG for the example of FIG. 137, accordingto some embodiments.

FIG. 147 is a local condition DAG for the example of FIG. 137 innavigation at node 84, after application of Merge Disjuncts (and lateroperations), according to some embodiments.

FIG. 148 is a final local DAG for the example of FIG. 137 in navigationat node 81, according to some embodiments.

FIG. 149 is a final local DAG for the example of FIG. 137 in navigationat node 82, according to some embodiments.

FIG. 150 is a final local DAG for the example of FIG. 137 in navigationat node 83, according to some embodiments.

FIG. 151 is a final local DAG for the example of FIG. 137 in navigationat node 84, according to some embodiments.

FIG. 152 is a final local DAG for the example of FIG. 137 in navigationat node 85, according to some embodiments.

FIG. 153 is the final global DAG for the example of FIG. 137, with arcslabeled with directives for reducing the data item set, according tosome embodiments.

FIG. 154 is a second initial global example DAG for describing therepresentation of conditions in data measure problems, according to someembodiments.

FIG. 155 is a local condition DAG for the example of FIG. 154 innavigation at node 90, according to some embodiments.

FIG. 156 is a local condition DAG for the example of FIG. 154 innavigation at node 91, before application of Conjoin Disjuncts,according to some embodiments.

FIG. 157 is a local condition DAG for the example of FIG. 154 innavigation at node 91, after application of Conjoin Disjuncts (and lateroperations), according to some embodiments.

FIG. 158 is a local condition DAG for the example of FIG. 154 innavigation at node 92, before application of Embed Conjunction,according to some embodiments.

FIG. 159 is a local condition DAG for the example of FIG. 154 innavigation at node 92, after application of Embed Conjunction (and lateroperations), according to some embodiments.

FIG. 160 is the final global DAG for the example of FIG. 154, accordingto some embodiments.

FIG. 161 is an alternate version of the final global DAG for the exampleof FIG. 154, using movement operator nodes, according to someembodiments.

FIG. 162 is a final local DAG for the example of FIG. 154 in navigationat node 93, according to some embodiments.

FIG. 163 is a project screen for the social innovation example withinitial problem and solution, according to some embodiments.

FIG. 164 is a user screen with a specializing problem not yet related tothe first, according to some embodiments.

FIG. 165 is a project screen selecting the operation of applying tospecialize a problem, according to some embodiments.

FIG. 166 is a project screen showing the now-related externalgeneralizing problem and inherited solution, according to someembodiments.

FIG. 167 is a project screen after the inherited solution has beenrestated and additional augmentation applied, according to someembodiments.

FIG. 168 is a user screen with a generalizing problem not yet related,according to some embodiments.

FIG. 169 is a project screen selecting the operation of inviting anotherproblem to specialize, according to some embodiments.

FIG. 170 is the specializing project screen dependencies tab after thesocial innovation example, according to some embodiments.

FIG. 171 is the specializing project screen ecosystem tab after thesocial innovation example, according to some embodiments.

FIG. 172 presents the high-level structure of the recommendationprocess, according to some embodiments.

FIG. 173 presents a sample user interface for associating state machineswith problems, according to some embodiments.

FIG. 174 presents a sample user interface for interacting with solutionsbased on their state, according to some embodiments.

Drawing elements in FIG. 1 through FIG. 174 may be assigned a four-digitcode as follows:

-   -   The first digit indicates the direction of refinement        augmentation and whether the embodiment deals with inheritance.        -   1: Primarily supporting specialization on non-inherited            nodes and explicit augmentation        -   2: Primarily supporting specialization on inherited nodes            and implicit augmentation        -   3: Primarily supporting specialization without regard to            inheritance        -   4: Primarily supporting generalization on non-inherited            nodes and explicit augmentation        -   5: Primarily supporting generalization on inherited nodes            and implicit augmentation        -   6: Primarily supporting generalization without regard to            inheritance        -   0: Applies without regard to inheritance or direction of            refinement augmentation    -   The second digit refers to whether the element is primarily        related to the client or the server in the presented embodiment.        -   1: Primarily for client        -   2: Primarily for server        -   0: Either    -   The third digit is sequential.    -   The final digit refers to relevant operation.        -   0: Initialization        -   1: Refinement Augmentation        -   2: Refinement/Cross-kind Augmentation        -   3: Any Augmentation        -   4: Deletion/Unlinking        -   5: Moving/Copying        -   6: Linking via Refinement            The numbering system is intended to aid intuition and refers            to a particular embodiment presented here. It is not            intended to limit the applicability of any routine.

FIG. 175 is a diagram displaying the representation of substructureinformation for a single entity in an embodiment.

FIG. 176 is a process flow diagram of an embodiment of the substructureconstruction process as described with respect to the Static LifetimeStrategy, according to some embodiments.

FIG. 177 is a process flow diagram of an embodiment of the substructureinitialization process as described with respect to the Static LifetimeStrategy, according to some embodiments.

FIG. 178 is a process flow diagram of an embodiment of the substructureexpansion process, as described with respect to the Static LifetimeStrategy, according to some embodiments.

FIG. 179 is a process flow diagram of an embodiment of the substructurecollapse process, according to some embodiments.

FIG. 180 is a process flow diagram of an embodiment of the maximalsubstructure expansion process under the assumption that child nodeswill not conflict, as described with respect to the Static LifetimeStrategy, Initialization Strategy #1, and Explicit Node ExpansionStrategy #1, according to some embodiments.

FIG. 181 is a process flow diagram of an embodiment of the substructureexpansion process that expands until any common descendants are reached,as described with respect to the Static Lifetime Strategy,Initialization Strategy #2, and Explicit Node Expansion Strategy #2,according to some embodiments.

FIG. 182 is a process flow diagram of an embodiment of the substructureexpansion process for initialization that opens single nonleaf childrenunder the assumption that child nodes will not conflict, as describedwith respect to the Static Lifetime Strategy, Initialization Strategy#3, and Explicit Node Expansion Strategy #3, according to someembodiments.

FIG. 183 is a process flow diagram of an embodiment of the substructureexpansion process for initialization that opens single children underthe assumption that child nodes will not conflict, as described withrespect to the Static Lifetime Strategy, Initialization Strategy #4, andExplicit Node Expansion Strategy #4, according to some embodiments.

FIG. 184 is a process flow diagram of an embodiment of the unarysubstructure expansion process for initialization under the assumptionthat child nodes will not conflict, as described with respect to theStatic Lifetime Strategy, Initialization Strategy #5, and Explicit NodeExpansion Strategy #5, according to some embodiments.

FIG. 185 is a process flow diagram of an embodiment of the portion ofthe maximal substructure expansion process that hides conflictingvisible nodes as described with respect to the Static Lifetime Strategyand Explicit Node Expansion Strategy #1 and Explicit Node ExpansionStrategy #2, according to some embodiments.

FIG. 186 is a process flow diagram of an embodiment of a portion ofcertain substructure expansion processes (that open single children orsingle nonleaf children) that hides conflicting visible nodes asdescribed with respect to the Static Lifetime Strategy, InitializationStrategy #4, and Explicit Node Expansion Strategy #4, according to someembodiments.

FIG. 187 is a diagram displaying the representation of contextinformation for a single entity in an embodiment.

FIG. 188 is a process flow diagram of an embodiment of the contextinitialization process for a single entity as described with respect tothe Dynamic Lifetime Strategy, according to some embodiments.

FIG. 189 is a process flow diagram of an embodiment of the contextexpansion process, as described with respect to the Dynamic LifetimeStrategy and Parent Node Reordering Strategy #2, according to someembodiments.

FIG. 190 is a process flow diagram of an embodiment of the contextcollapse process for a single entity as described with respect to theDynamic Lifetime Strategy, according to some embodiments.

FIG. 191 is a process flow diagram of an embodiment of the maximalcontext expansion process under the assumption that child nodes will notconflict, as described with respect to the Dynamic Lifetime Strategy,Initialization Strategy #1, and Explicit Node Expansion Strategy #1,according to some embodiments.

FIG. 192 is a process flow diagram of an embodiment of the substructureexpansion process that expands up until any common ancestor is reached,as described with respect to the Dynamic Lifetime Strategy,Initialization Strategy #2, and Explicit Node Expansion Strategy #2,according to some embodiments.

FIG. 193 is a process flow diagram of an embodiment of the contextexpansion process for a single locus entity that opens single nonleafchildren under the assumption that child nodes will not conflict, asdescribed with respect to the Dynamic Lifetime Strategy, InitializationStrategy #3, and Explicit Node Expansion Strategy #3, according to someembodiments.

FIG. 194 is a process flow diagram of an embodiment of the contextexpansion process that opens single children under the assumption thatchild nodes will not conflict, as described with respect to the DynamicLifetime Strategy, Initialization Strategy #4, and Explicit NodeExpansion Strategy #4, according to some embodiments.

FIG. 195 is a process flow diagram of an embodiment of the unary contextexpansion process under the assumption that parent nodes will notconflict, as described with respect to the Dynamic Lifetime Strategy,Initialization Strategy #5, and Explicit Node Expansion Strategy #5,according to some embodiments.

FIG. 196 is a process flow diagram of an embodiment of the portion ofthe maximal context expansion process that hides conflicting visiblenodes as described with respect to the Dynamic Lifetime Strategy andExplicit Node Expansion Strategy #1 and Explicit Node Expansion Strategy#2, according to some embodiments.

FIG. 197 is a process flow diagram of an embodiment of a portion ofcertain context expansion processes (that open single parents or singlenonorphan parents) that hides conflicting visible nodes as describedwith respect to the Dynamic Lifetime Strategy, Initialization Strategy#4, and Explicit Node Expansion Strategy #4, according to someembodiments.

FIG. 198 is a diagram displaying the representation of contextinformation that can be shared across multiple entities in anembodiment.

FIG. 199 is a screen with multiple locus skills, demonstratingexploration of their shared context, according to some embodiments.

FIG. 200, FIG. 201, and FIG. 202 are screens with multiple locus skills,demonstrating opening of context folders with shared context, accordingto some embodiments.

FIG. 203 is a screen with multiple locus skills, demonstrating theclosing of a context folder with shared context, according to someembodiments.

FIG. 204 is a process flow diagram of an embodiment of the contextinitialization process for multiple entities as described with respectto the Dynamic Lifetime Strategy, according to some embodiments.

FIG. 205 is a process flow diagram of an embodiment of the contextcollapse process for multiple entities as described with respect to theDynamic Lifetime Strategy, according to some embodiments.

FIG. 206 is a process flow diagram of an embodiment of the contextexpansion process for multiple locus entities that opens single nonleafchildren under the assumption that child nodes will not conflict, asdescribed with respect to the Dynamic Lifetime Strategy, InitializationStrategy #3, and Explicit Node Expansion Strategy #3, according to someembodiments.

FIG. 207 is a process flow diagram of an embodiment of the contextexpansion process for multiple locus entities that opens single childrenunder the assumption that child nodes will not conflict, as describedwith respect to the Dynamic Lifetime Strategy, Initialization Strategy#4, and Explicit Node Expansion Strategy #4, according to someembodiments.

FIG. 208 is a process flow diagram of an embodiment of the unary contextexpansion process under the assumption that parent nodes will notconflict, as described with respect to the Dynamic Lifetime Strategy,Initialization Strategy #5, and Explicit Node Expansion Strategy #5,according to some embodiments.

FIG. 209 is a process flow diagram of an embodiment of a portion ofcertain context expansion processes (that open single parents or singlenonorphan parents) that hides conflicting visible nodes as describedwith respect to the Dynamic Lifetime Strategy, Initialization Strategy#4, and Explicit Node Expansion Strategy #4, according to someembodiments.

FIG. 210 is a process flow diagram of an embodiment of a portion of thecontext expansion processes for multiple locus entities that hidesconflicting visible nodes by raising their DAG descendants to top levelas described with respect to the Dynamic Lifetime Strategy, according tosome embodiments.

FIG. 211 is a process flow diagram of an embodiment of a portion of thecontext expansion processes for multiple locus entities that capturestop-level nodes whose parent set is revealed during expansion asdescribed with respect to the Dynamic Lifetime Strategy, according tosome embodiments.

FIG. 212 is a diagram displaying the representation of substructureinformation that can be shared across multiple entities in anembodiment.

FIG. 213 is a process flow diagram of an embodiment of a routine thataccepts a path of entity identifiers from a point in the substructure tothe root and ensures that nodes along that path are unfolded, accordingto some embodiments.

FIG. 214 is a process flow diagram of an embodiment of a routine thataccepts a path of entity identifiers from a point in the context to theroot and ensures that nodes along that path are unfolded, according tosome embodiments.

FIG. 215 is a project screen with active auxiliary information relatedto both context and substructure, according to some embodiments.

FIG. 216 is a project screen with auxiliary information related tocontext node, according to some embodiments.

FIG. 217 is a project screen with auxiliary information related to locusnode, according to some embodiments.

FIG. 218 is a project screen with auxiliary information related to firstsubstructure node, according to some embodiments.

FIG. 219 is a project screen with auxiliary information related to thesecond substructure node, according to some embodiments.

FIG. 220 is a project screen with auxiliary information related to thethird substructure node, according to some embodiments.

FIG. 221 is a project screen with active auxiliary information relatedto context, according to some embodiments.

FIG. 222 is a project screen with active auxiliary information relatedto substructure, according to some embodiments.

FIG. 223 is a project screen with active auxiliary information relatedto locus node, according to some embodiments.

FIG. 224 is a project screen with constituent auxiliary informationrelated to the second substructure node, according to some embodiments.

FIG. 225 is a project screen with constituent auxiliary informationrelated to the third substructure node, according to some embodiments.

FIG. 226 is a project screen with constituent auxiliary informationrelated to substructure, according to some embodiments.

FIG. 227 is a process flow diagram of an embodiment of the clientprocess to select a facet value by which entities are to be included aslocus nodes, according to some embodiments.

FIG. 228 is a process flow diagram of an embodiment of the clientprocess to deselect a facet value by which entities are to be includedas locus nodes, according to some embodiments.

Each drawing element in FIG. 175 through FIG. 228 is assigned asix-digit code as follows:

-   -   The first digit refers to relative position.        -   1: Substructure        -   2: Context    -   The second digit refers to the nodes that are active with        respect to a state of navigation.        -   1: Single Locus Node        -   2: Multiple Locus Nodes        -   3: Uniform Nodes        -   0: Relevant to more than one focus    -   The third digit refers to the operation with which the element        is most closely associated.        -   1: create        -   2: expand        -   3: collapse        -   4: remove        -   0: Relevant to multiple operations    -   The fourth digit refers to whether the nodes are statically or        dynamically allocated (as described with respect to the Lifetime        Strategies).        -   1: Static        -   2: Dynamic    -   The fifth digit refers to a strategy for how much content should        be revealed, or 0 for any or N/A, in the order listed with        respect to the Initialization Strategies or the Explicit Node        Expansion Strategies:    -   The final digit is sequential.        The numbering system is intended to aid intuition and refers to        a particular embodiment presented here. It is not intended to        limit the applicability of any routine.

FIG. 229 is a user screen not checked into any project role, accordingto some embodiments.

FIG. 230 is a user screen selecting the operation of checking in to anew project role, according to some embodiments.

FIG. 231 is a user screen selecting the operation of checking out fromthe current project role, according to some embodiments.

FIG. 232 is a process flow diagram of an embodiment of the process tohandle a change request, according to some embodiments.

FIG. 233 is a process flow diagram of an embodiment of the process toapprove a change, according to some embodiments.

FIG. 234 is a process flow diagram of an embodiment of the process toreject a change, according to some embodiments.

FIG. 235 is a process flow diagram of an embodiment of the process torollback a change, according to some embodiments.

FIG. 236 is a process flow diagram of an embodiment of the process toundo a rollback, according to some embodiments.

DETAILED DESCRIPTION

There has been recognition of the value of a separation of the “problemspace” from the “solution space” with respect to a project. Elements ofthe problem space may be referred to as “problems” or “challenges”, andelements of the solution space as “solutions” or “approaches”. Varioussystems facilitate collaboration and/or innovation by allowing for theproposal of challenges and potential solutions that address thosechallenges.

We interpret problems and solutions broadly, to apply to any domainincluding broad societal problems and solutions that could alleviatethem, technical or engineering problems and solutions that satisfy them,and problems identified by marketing efforts as customer pain points andsolutions as new products that could relieve them.

One can seek analogies for problem and solutions spaces in programminglanguages theory. For example, problems might correspond to types andsolutions correspond to expressions, with the assignment of a type to anexpression corresponding to a solution addressing a problem. Thisanalogy is unsatisfying, because while a solution necessarily solves anyspecial case of a problem it addresses, an expression belonging to atype does not necessarily belong to any subtype of that type. It's notthat type theory isn't relevant, but rather that the relationship iscontravariant. In particular, when one problem refines another, we meanthat the latter problem can be seen as a function type with a morespecific domain. For example, the problem of reducing poverty in anurban setting refines the problem of reducing poverty more generallybecause the urban setting is more specific than a more general setting,and one can make use of features of that setting in crafting a solution.

Object-oriented languages provide an analogy for such situations,because classes are in a refinement hierarchy where one method parameter(generally called “this” or “self”) relates to the position in thehierarchy and thus becomes more specific at lower levels. Just as amethod at a superclass can be called by any subclass, a solution to arefined problem applies to any refining problems, but the converse (amethod at a subclass being called from a superclass) is not generallysafe. Notice that we consistently use “refining” to refer to the morespecialized entity and “refined” to refer to the more general one thatit refines, which may differ from some common usage.

In programming languages theory there is a notion of refinement ofexpressions, whereby one expression refines another if it terminateswhenever the refined expression does and with the same result. There isalso a notion of refinement of expressions by a homomorphic mapping fromthe state diagram of the refining expression to that of the refinedexpression.

In terms of projects, refinement of a problem can correspond toidentification of a special case of a problem and refinement of asolution can correspond to elaboration of the solution with additionaldetail. In addition to the relation of a solution addressing a problem,we consider the relation of a solution motivating a problem, wherebyimplementing a solution to a motivated problem would contribute towardsimplementing the motivating solution. We consider inheritance ofsolutions through the refinement relation on problems as well asinheritance of problems through the refinement relation on solutions.Inheritance of a solution through the refinement relation on problemsrecognizes that a solution to a problem is also relevant to anyrefinements of that problem, although a refining solution may be moreappropriate. Inheritance of a problem through the refinement relation onsolutions recognizes that a problem whose solution is necessary forimplementing a motivating solution is also relevant to implementing anyrefinement of that solution and must be addressed, although perhaps inthe form of a refining problem. In general, both the refinement relationon problems and that on solutions are many-to-many relations, i.e., notonly can the same problem or solution be refined in multiple ways, but agiven problem or solution can refine multiple other problems orsolutions, respectively. The relations of a solution addressing andmotivating a problem may also be many-to-many relations.

It is often the case but not appreciated that a solution is refined withrespect to a problem, i.e., the additional detail provided is related tothe fact that the refining solution addresses a refining problem. Orfrom another perspective, a solution to a problem may leverage off of aless specific solution to a more general problem. Likewise, it is oftenthe case but not appreciated that a problem is refined with respect to asolution, i.e., the special case identified is related to the fact thatthe refining problem is motivated by a refining solution that moretightly defines what needs to be accomplished. Or alternatively, aproblem motivated by a solution may add qualifications to a more generalproblem motivated by a less specific solution.

Beyond solutions addressing problems and problems motivated bysolutions, embodiments maintain information about other elements ofproject information, which may include, without limitation, skills,arguments, individuals, and funds. For example, one can maintain skillsrequired by a solution, with more specific solutions requiring morespecific skills, and similarly arguments supporting or opposing problems(their relevance), solutions (their correctness), or other arguments(their validity). Required skills may be inherited through therefinement relation on solutions. Moreover, a skill may be refined withrespect to a solution. Various elements of project information supportnatural refinement relations and inheritance of project informationalong those refinement relations in various directions. For example,requiring projects and proficient individuals may be inherited upwardthrough the subskill refinement relation.

Augmentation of a hierarchy in a top-down manner may be supported byproviding problems or solutions that refine those already present,solutions that address problems already present, and problems that aremotivated by solutions already present. A hierarchy may conversely beaugmented in a bottom-up manner. It would be useful to have an intuitivemeans of augmenting a DAG representing a project that implicitlycaptures facts such as that a solution of a problem may be defined withrespect to a solution of a refined problem and that a problem motivationmay be defined with respect to a refined problem motivation, what wewill call relative DAG augmentation. Such a facility could also maintaina refinement correspondence between associations, so that latermodifications to the project structure can be treated appropriately.

Information may often be presented with respect to an acyclic parentrelation among entities. The converse of the parent relation is thechild relation. Entities, here, may be physical or conceptual. Byacyclic, we mean that no chain of one or more applications of therelation from any entity will yield that same entity. Such relation may,for example, represent that one entity or concept dominates, subsumes,or gave rise to another. As a few more specific examples: sets can beseen as parents of sets with strictly fewer elements; interfaces orclasses in traditional object-oriented languages, or instances indelegation-based object-oriented languages are related by a hereditarystructure; individuals (or portions of their genome) are related totheir biological parents; in an outline structure of a document, anydeclared section of the document can be seen as a parent of each of itssubdivisions; versions of a document are children of the prior versionsfrom which they were developed. A tree is a hierarchical structure inwhich an entity has at most one parent. More generally, a directedacyclic graph (DAG) is a hierarchical structure in which an entity mayhave any number of parents. With respect to traditional object-orientedlanguages, classes in a Java program form a tree structure, whileinterfaces in a Java program and classes in C++ and Python programs allsupport multiple inheritance and thus form DAG structures. A non-emptytree has a single root node, having no parents. A non-empty DAG has oneor more root nodes, having no parents. A node with no children isreferred to as a leaf; a node with no parents is referred to as anorphan. A multiplicity of non-empty trees or DAGs is referred to as aforest or DAG-forest, respectively. The siblings of a DAG or tree nodeare the other children of its parents. The anti-siblings of a DAG nodeare the other parents of its children. To avoid confusion, we refer tosiblings in the context tree, which are anti-siblings in the underlyingDAG and the substrate tree, as context siblings. For the remainder ofthis description, we will use node only with respect to trees andconsider the underlying DAG to be a conceptual relationship amongentities.

A hierarchical structure may be large, so that it is difficult for anobserver to orient themselves to its most relevant contents. Trees maybe visualized with child nodes indented below their parents. There arestandard and generally accepted ways of focusing on portions of trees,by collapsing and expanding various nodes. Those nodes may berepresented with icons such as open, closed, or perhaps empty folders,that represent the current state of focus of that portion of the tree.An open folder might represent that the node has been expanded so thatits children are visible; a closed folder that the node has beencollapsed so that its children are hidden; an empty or upside-downfolder that the node represents an entity without children. We speak ofopening or closing the context or substructure of a node as marking thatnode appropriately to express the appropriate focus with respect to thathierarchy. Some embodiments may choose to support only open and closedicons, allowing nodes representing entities without descendants to be inan open or closed state.

DAGs may be visualized as their underlying graph, such that all edgespoint in the same general direction. This is used, for example, inopen-source tools that support visualization of the evolution of variousversions of a file system, including branching and merging of versions.But a DAG can be complex and distracting to represent visually. A treeis conceptually simpler than a DAG, and it may be the case that only oneor a few subtrees within a DAG are relevant at any point in time. Itwould be useful to have a way of focusing in a DAG as if it were a tree,by designating one or more locus nodes to which users may navigate andwith respect to which they may collapse and expand nodes, such that anyentity is only represented by a single node in the visualization at anypoint in time. Another advantage of the tree representation is that itenables the use of common idioms such as copying, cutting, and pastingportions of DAGs.

We present various definitions relevant to describing some embodimentssupporting navigation to locus nodes. The full subtree rooted at a nodewithin a tree is composed of all of the nodes reachable from that nodevia the child relation; its context is the path from the node to theroot. Similarly, the full subDAG rooted at a node within a DAG iscomposed of all of the nodes reachable from that node via the childrelation; its context is the inverted tree rooted at that node andcontaining nodes reachable by any number of applications of the parentrelation. We generally consider context to include the locus node andrefer to proper context if we wish to exclude the locus node. Thesubstructure of a full subtree or full subDAG are all of the nodescontained therein. We generally consider substructure to include thelocus node and refer to proper substructure if we wish to exclude thelocus node. Both the substructure and the context form logical trees;their components are also referred to as logical. This distinguishesthem from the substrate trees in which they are represented, whosecomponents are also referred to as substrate. Context grows upwardswhile substructure grows downwards. Substrate trees always growdownwards. These definitions are for expository purposes only. The onlytrees that must exist explicitly in embodiments in some form are theones visualized by a user who is enabled to explore them. Such trees maybe created by indenting nodes appropriately, forgoing all of theseintermediate representations.

Systems supporting navigation of a tree and having a notion of locusnode within the tree often provide access to the context of the subtreerooted at that node as a sequence of nodes in a parent relation, up tothe root of the tree. For example, an operating system shell may displayin its prompt the sequence of parent directories leading back to somedesignated root or home directory. It would be useful to have a way ofvisualizing and focusing on the context of a subDAG within a DAG, againsuch that any entity is only represented by a single node in thevisualization at any point in time. One approach is to displayseparately the substructure tree and the context tree, both growingdownward, and allowing both to be manipulated as simple trees, but thisis not satisfying as it does not provide the user with a sense of theplace of the locus entity as existing between the substructure and thecontext.

HTML is well-suited for representing trees as nested lists, and browsershave standard ways of visualizing such tree structures. Otherrepresentation languages including JSON are similarly well-suited forrepresenting trees. It is clearly possible to represent a subtree andits context within the full tree as a single tree with the same root asthe full tree, by excluding any nodes not in the subtree or the path tothe root. It would be useful to have a way of visualizing portions ofthe substructure and context of a subDAG within a DAG as a single treethat could be presented within a substrate such as HTML.

Moreover, given a multiplicity of subDAGs (each rooted at differentlocus node), it would be useful to see them presented so that variousconnections to common ancestors and descendants are manifest.

Version control systems may be sequential in that they treat a revisionhistory as a sequence of “commits”. Each of those commits can includemultiple changes to the same or various files. The changes within a fileare identified by recognizing differences between an old and new versionof the file. Those changes are committed together and while it is alwayspossible to tease them apart later into separate commits, that is notthe intended use. Rather, commits are intended to be undone one at atime, in the reverse order that they were established. Commits arerecorded as “diff” results that notate which lines of a file are to bereplaced with which other lines. It is thus easy to apply the diffs tothe original file to bring it in line with the modified file, or viceversa. It is more difficult to apply “diff”s to a modified version ofeither file and this process may result in conflicts that must beresolved by a user.

Standard “diff” files are somewhat arbitrary in that there may be morethan one way of recording a change to a file. In an extreme example,where the initial file contains 1000 identical lines and the revised one999 of these lines, any one could have been assumed to have beendeleted. The difference may matter if the diff file is later applied toa modified version of the original file.

Furthermore, chains of commits in standard version control form branchesthat may split and merge in a DAG. Thus, it is possible for a user toestablish parallel branches with different changes, and undo thosechanges separately. But each branch contains only one set of changes,and if the branches are eventually merged, we again have a linearsequence of commits to deal with.

It is possible in standard version control to update a commit in themiddle of a sequence and to then play back the subsequent commits,possibly triggering conflicts during this process. Such conflicts can bedifficult to manage and resolve, but requiring that modifications beundone in the reverse order to that in which they were applied is overlyrestrictive when the changes are independent.

It would be useful to have a hierarchical system of version control thatnaturally arranges changes not in a linear sequence but in a DAG.

On conflicting changes to a database record, standard practice ofteninvolves rejecting all but one of the proposed changes. It would beuseful to have a hierarchical system of version control that maintainsand organizes conflicting changes for orderly conflict resolution.

A Method Using Inheritance to Support the Augmentation of ProjectHierarchies

Project Management Entities and Relationships Including Separation ofProblem and Solution Spaces

Embodiments construct DAGs (possibly trees) based on various givenintuitively acyclic relations. For many kinds of entities, there arenatural refinement relations, such as the following:

-   directlyRefinesProblem To a problem, from one of its refining    problems, i.e., a special case of the first problem.-   directlyRefinesSolution To a solution, from one of its refining    solutions, i.e., another solution consistent with that solution, but    adding more detail.-   directlyRefinesSupportingArgument To a supporting argument, from one    of its refining supporting arguments, i.e., another supporting    argument consistent with the first, but adding more detail or taking    a stronger position.-   directlyRefinesOpposingArgument To an opposing argument, from one of    its refining opposing arguments, i.e., another opposing argument    consistent with the first, but adding more detail or taking a    stronger position.-   directlyRefinesSkill To a skill, from one of its refining skills,    i.e., a specialization of the first skill (i.e., a subspecialty, or    subskill), such as from coronary surgery to surgery.-   directlyRefinesUser To a user, from one of its refining users, e.g.,    a mentee or a subordinate in an organizational chart of the first    user.

There are also often natural cross-kind relations among entities, suchas the following:

-   directlyAddresses From a solution to a problem it addresses. It is    natural (but not necessary) to require that every solution addresses    at least one problem.-   directlyMotivatedBy From a problem to a solution that motivates it    (a solution to the problem would contribute towards implementing the    given solution).-   directlySupports To a problem, solution, or supporting or opposing    argument, from an argument that supports it.-   directlyOpposes To a problem, solution, or supporting or opposing    argument, from an argument that opposes it.-   directlyRequiredBy From a skill to a solution that requires it.-   directlyProficientInSkill From a user proficient in a skill to that    skill. Associations under this relation may be annotated with a    proficiency level.    Any of these relations may be available as the basis for creation of    a DAG structure. Various embodiments may make use of more or fewer    relations, including these or any other naturally acyclic relations.    These relations may be many-to-many, or any of them may be    restricted to be many-to-one. If all are so restricted, the    generality of a DAG is unnecessary as a tree would suffice for that    relation, although the union of several such relations could still    be many-to-many. In some cases (particularly the latter two)    embodiments may well wish to build DAGs based either on the stated    relation or its inverse.

In a cross-kind relation such as directlyAddresses, directlyMotivatedBy,directlySupports, directlyOpposes, or directlyRequiredBy, we refer tothe first argument as the dependent entity and the second as theindependent entity, with the intention that it be possible to inherit adependent entity through a refinement chain of independent entities. Werefer to an independent entity associated under such a relation with adependent entity as an object of that dependent entity.

We use “refinement relation” to refer to any relation that can supportinheritance (generally inheritance of dependent entities and, perhaps,their descendants), from a refined independent entity to any of itsrefining entities. We will see below under “In-place, Iterating DAGAugmentation” as “inherit other refining nodes through a restatement”that a refinement relation that is a restatement may also supportinheritance of refining entities under that or another refinementrelation. We use “cross-kind” relation to refer to any non-refinementrelation, regardless of whether the kinds of entities related areactually the same or not. Embodiments may support only one refinementrelation between entities of the same kind, or multiple such refinementrelations. Embodiments such that only relation exists between entitiesof a pair of kinds (not necessarily distinct) may assume that all suchassociations between entities of those kinds are due to that relation.

We can then generate various derived relations. We begin with somestandard technical definitions of derived relations:

-   -   We use the infix operator; to indicate composition of two        relations, i.e., such that a pair of elements are related if        there exists a third element such that the first is related to        the third by the first relation and the third is related to the        second by the second relation. The composition of relations has        number no more than one-to-one if both relations are one-to-one.        The composition of relations has number no more than one-to-many        if the relations being composed are one-to-many or one-to-one.        The composition of relations has number no more than many-to-one        if the relations being composed are many-to-one or one-to-one.        The composition of relations may be many-to-many only if at        least one relation being composed is each of one-to-many and        many-to-one, or if at least one relation being composed is        many-to-many.    -   We use the postfix operator Kleene star (_*) to indicate the        composition of zero or more applications of the supplied        relation (from one kind to the same kind). The result of a        Kleene star operation has the same number as its argument.    -   We use the postfix inverse operator (_⁻¹) to indicate the        relation with all arrows reversed from the argument relation        (for a cross-kind relation, the input and output kinds are        reversed).

It is useful to extend these directly defined relations in natural ways.Clearly, for the refinement relations:

refinesProblem:=directlyRefinesProblem*

refinesSolution:=directlyRefinesSolution*

refinesSupportingArgument:=directlyRefinesSupportingArgument*

refinesOpposingArgument:=directlyRefinesOpposingArgument*

refinesSkill:=directlyRefinesSkill*

refinesUser:=directlyRefinesUser*

refinedByProblem:=refinesProblem⁻¹

refinedBySolution:=refinesSolution⁻¹

refined BySupportingArgument:=refinesSupportingArgument⁻¹

refined ByOpposingArgument:=refinesOpposingArgument⁻¹

refinedBySkill:=refinesSkill⁻¹

refinedByUser:=refinesUser⁻¹

In some cases, we may require that every dependent entity be related toone or more independent entities. For example, we might require thatevery solution address one or more problems, or that every argumentsupport or oppose one or more objects. We would not likely require thatevery problem be motivated by one or more solutions or that every skillbe required by one or more projects. In some cases, we may require thatevery dependent entity be related to exactly one independent entity.Depending on the kind of entities and the relationship beingrepresented, we may wish to enforce various other constraints on therelationships.

For the cross-kind relations, we begin with the obvious:

directlyAddresses⊆addresses

directlyMotivatedBy⊆motivated By

directlySupports⊆supports

directlyOpposes⊆opposes

directlyRequiredBy⊆requiredBy

and then notice the following basis for inheritance:

-   addresses; refinedByProblem⊆addresses A solution is assumed to    address all refinements of any problem that it addresses. A problem    is assumed to be addressed by any solution that addresses any    problem it refines.-   motivated By; refinedBySolution⊆motivated By A problem is assumed to    be motivated by all refinements of any solution that motivates it. A    solution is assumed to motivate any problem that is motivated by any    solution it refines.-   supports; refinedByObject⊆supports An argument is assumed to support    all refinements of any objects that it supports. An object is    assumed to be supported by any argument that supports any object it    refines.-   opposes; refinedByObject⊆opposes An argument is assumed to oppose    all refinements of any objects that it opposes. An object is assumed    to be opposed by any argument that opposes any object it refines.-   requiredBy; refinedBySolution⊆requiredBy A skill is assumed to be    required by all refinements of any solution that requires it. A    solution is assumed to require any skill that is required by any    solution it refines.

When one entity refines another, dependent entities associated with theentity being refined are also associated with the refining entity. Thus,when a user has navigated to a particular entity, it makes sense to showthem entities directly dependent on entities which they refine. We callthese inherited entities. For example, the problem “How can we establisha reduction in poverty?” can be created as a root problem and refined to“How can we establish a reduction in rural poverty?” and to “How can weestablish a reduction in poverty among able-bodied individuals?”. FIG. 1through FIG. 6 show an embodiment supporting these actions. FIG. 1 is aninitial Teamifier user page with a button (when the active user viewstheir own page) for creating a new “challenge” (the system uses“challenge” for “problem” and “approach” for “solution”). Clicking thebutton provides (as in FIG. 2) an input field for the user to enter theessence of their problem, e.g., what they'd like to see established. InFIG. 3 the field is filled. Upon leaving the entry field, a transactionis sent to the server and if a response indicating success is received,a link to a challenge page is created as in FIG. 4. Clicking on the linkcreated for the root problem takes a user to that problem's page, fromwhich they could create the refining problems. FIG. 5 shows theselection of a specialization operation and FIG. 6 entry of the firstspecializing problem. “Let's teach needy people a skill!” might be addedas a solution addressing the problem, “How can we establish a reductionin poverty?”, so that solution necessarily applies as well to theserefining problems, although as we will see, refining solutions may behelpful. FIG. 7 through FIG. 9 demonstrate how a user might propose thesolution (after both specializing problems have been created). FIG. 7shows the selection of the solving operation and FIG. 8 the entry ofthis solution. FIG. 9 shows the page after the solution has beencreated. FIG. 10 shows the selection of the componentizing operation forthe new solution, FIG. 11 the entry of “How can we establish what thepeople already know?” as a component problem. Now, clicking on the linkfor one of the refining solutions, the user would see as in FIG. 12 thesolution and its component as inherited descendants (indicated here withgray icons) as well as the general problem as context (also indicatedhere with gray icons). Likewise, a solution, “Let's transport suppliesto where they are needed!” can be refined to “Let's transport suppliesby submarine!” and to “Let's transport materials by spaceship!”. “Howcan we establish protection of the supplies during transit?” might be aproblem motivated by the solution, “Let's transport supplies to wherethey are needed!”, so solving that problem would necessarily contributeto a solution to those refining solutions, although as we will see,refining problems may be helpful. FIG. 13 shows the result of clickingon the second solution specialization, with the general problem'scomponent problem as an inherited child node.

We further notice the following basis for inheriting refining objects.

-   refinesSolution; addresses⊆addresses Any problem addressed by a    solution is also addressed by the solution's refinements. A solution    addresses any problem addressed by a solution it refines.-   refines Problem; motivated By⊆motivated By Any solution that    motivates a problem also motivates the problem's refinements. A    problem is motivated by any solution that motivates a problem it    refines.-   refinesSupportingArgument; supports⊆supports Any object supported by    an argument is also supported by the argument's refinements. An    argument supports any object supported by an argument it refines.-   refinesOpposingArgument; opposes⊆opposes Any object opposed by an    argument is also opposed by the argument's refinements. An argument    opposes any object opposed by an argument it refines.-   refinesSkill⁻¹; requiredBy⊆requiredBy Any solution that requires a    skill also requires the skill's generalizations.

A skill is required by any solution that requires a skill that refinesit.

Notice that the refinement relation acts in the opposite direction inthe inclusion for skill requirements by a solution; superskills ratherthan subskills of a skill are necessarily required by refinements ofsolutions requiring that skill.

When a user has navigated to a particular entity, we show them entitiesnot only directly dependent on entities which they refine, and entitiesthat refine the dependent entities, but entities that are dependentthrough any series of direct dependencies and refinements.

Embodiments support a user, or multiple users collaboratively, indeveloping and extending DAGs based on entities and relations.

A solution of a problem may be defined with respect to one or moresolutions of refining problems. Likewise, a problem motivated by asolution may be defined with respect to one or more problems motivatedby refining solutions. For the example of “Let's teach needy people askill!” addressing the problem, “How can we establish a reduction inpoverty?”, “Let's teach needy people to farm!” both refines “Let's teachneedy people a skill!” and directly addresses the refining problems “Howcan we establish a reduction in rural poverty?” and “How can weestablish a reduction in poverty among able-bodied individuals?”. Goingfurther, “How can we establish what crops the people can already grow?”is a component of “Let's teach needy people to farm!” and specializes“How can we establish what the people already know?”. For the example of“How can we establish protection of the supplies during transit?” beinga problem motivated by the solution “Let's transport supplies to wherethey are needed!”, “How can we establish protection of the suppliesduring transit through diverse pressure conditions?” both refines “Howcan we establish protection of the supplies during transit?” and isdirectly motivated by refining solutions “Let's transport supplies bysubmarine!” and “Let's transport materials by spaceship!”. Suchaugmentation operations may be specified explicitly or implicitly by theuser. For the first example, FIG. 14 through FIG. 21 show ademonstration of user actions to create these project entities and theirresults. FIG. 14 shows the user initiating an operation to mutuallyspecialize “How can we establish a reduction in rural poverty?” and “Howcan we establish a reduction in poverty among able-bodied individuals?”.The user selects the former, marking it with a green boundary, andinitiates the specialization operation from the latter. We assume thatthe user creates the specializing problem and navigates to it, thenexpands the context. “How can we establish what the people alreadyknow?” is displayed as an inherited descendant of the new problem. Wewill present various formulations of the creation of a cross-kindassociation alongside one or more refinement associations. FIG. 15 showsthe initiation of a specialization operation from that inheriteddescendant, implicitly also requesting specialization of its inheritedparent, “Let's teach needy people a skill”. FIG. 16 shows an in-placerestatement by the user of “Let's teach needy people a skill!” to “Let'steach needy people to farm!” as a solution of that problem. The systemthen progresses to an in-place restatement in FIG. 17 by the user of“How can we establish what the people already know?” to “How can weestablish what crops the people can already grow?”. If the user thennavigates to the new solution and expands the context appropriately, wesee in FIG. 20 that the new problem is a child of both the problem itrefines, “How can we establish what the people already know?” and thesolution of which it is a component, “Let's teach needy people tofarm!”. We also see that the latter solution is a child of both thesolution it refines, “Let's teach needy people a skill!” and the problemit solves, “How can we establish a reduction in rural poverty amongable-bodied individuals?”. If the user navigates to the original generalproblem, “How can we establish a reduction in poverty?” andappropriately expands the substructure, we see in FIG. 21 that thesolution “Let's teach needy people a skill!” still exists as does itschild, “How can we establish what the people already know?”, and thateach of these has as a child its new restatement.

FIG. 22 shows how data flows through an embodiment. The DOM Tree existsonly on the client, while the Full DAG exists only on the server. Thelocalized DAG is created by the server for use by the client. Itincludes a subset of the information from the Full DAG from theperspective of one or more entities to which the client has navigated.All three data stores are maintained based on user operations generatedthrough the Client UI.

FIG. 23 shows possible sequencing of interactions between a client and aserver system under an embodiment. There could be any number of clientsystems interacting with the server, and either the client or the servercould potentially be distributed over many computing and storagedevices. We elide any serialization and unmarshalling of values fortransport, as this requirement is familiar to those skilled in the artof software development. The client might begin by presenting a searchquery to the server. The server might respond with zero or more searchresults, from which the client might select one or more locus entities.Alternatively, the client might navigate through a representation of thefull DAG to select one or more locus entities. This selection iscommunicated to the server, which localizes the DAG to those entitiesvia Localize DAG 2200. The resulting DAG is sent to the client, where itis set to be explored by the user with Present DAG 0100. At any pointnow, the server may notify the client of updates to the local DAGentities generated by other sessions, implementable through web sockets.The user may select one or more entities, repeating this processing onthe server side. Alternatively, the user may perform a manipulativeoperation on the DAG. If the user augments the DAG, in addition to theclient (via Client Specializing DAG Augmentation 2101 and ClientCross-kind and Specializing DAG Augmentation 2102) implementing thisoperation on its own copies of the DAG (including the user'svisualization) the parent entity ids and new entity information are sentto the server, which performs corresponding operations on the server'sDAG (via Specializing DAG Augmentation 3201 and Specializing Cross-kindDAG Augmentation 3202). Augmenting the DAG may involve augmenting aninherited node, in which case Copy Inheritance for Specialization 2103may be required. We have assumed here top-down augmentation, but ofcourse bottom-up could be handled similarly. If the user deletes aportion of the DAG Delete DAG Portion 0104, the server should benotified of that portion, perhaps by enumerating the entity ids to bedeleted. The client and server may delete those entities Delete Entity0204 and any connecting relationships Delete Relationship 0214(inherited entities are not subject to deletion). If parents andchildren of the deleted nodes remain in the DAG, they may be connectedby new relationships Create Relationship 0213. If the user unlinkschildren from their parents Unlink Entity 0114, the server is notifiedof the entity ids and their parent entity ids. The client and server maydelete those relationships on their own copies of the DAG DeleteRelationship 0214 (inherited entities are not subject to being unlinkedfrom their parents). If the user moves a portion of the DAG to newparents and children, replacing an existing relationship, Move DAGPortion 0105 the server is notified of the portion of the DAG so moved,its old parent and child entity ids and its new parent and child entityids. The client and server may delete the relationships linking thisportion of the DAG to its old parents Delete Relationship 0214 andcreate relationships linking it to its new parents Create Relationship0213. Again, if parents and children of the deleted nodes remain inplace in the DAG, they may be connected by new relationships. Theseoperations are defined broadly; an embodiment may provide special casesof any of them. Any number of other operations may be expressible by theuser through the client; each is performed on both client and servercopies of the DAG. In each case, operations may be communicated to theserver at any level of abstraction; e.g., analysis of the high-leveloperations may take place only on the client, or on both the client andthe server. The latter duplicates effort but may reduce transport costsand provide a more secure interface. For example, some embodiments mighthave each server operation create only a single entity or relationship,which are the underlying operations.

The terms client and server are to be interpreted broadly. The clientand the server may in some cases be the same machine. Moreover, theglobal DAG may be divided among any number of server systems. As anextreme case, each user may host the content of projects they administeron their own machine.

Explicit DAG Augmentation by Specialization

Some embodiments provide the user with a global view of the full DAG, orany restriction thereof. From this DAG, they can select nodes from whichthey wish to extend the DAG.

The user might select several entities of the same kind to jointlyrefine. Consider the DAG in FIG. 24, with circles representing entitiesof independent kind and squares representing entities of dependententity kind (we assume here and below for concreteness but without lossof generality that circles and squares represent problems and solutions,respectively, that links between the same shape represent refinement,and that links between circles and squares represent either a solutionaddressing a problem or a problem motivated by a solution, depending onthe direction). Here, we see a “diamond” refinement pattern amongproblems. If the user jointly refines nodes 4 and 10, the DAG in FIG. 29is a possible result.

The user might instead explicitly select both an independent entity toextend with a cross-kind association and any number of dependententities to refine. For example, the user might select a problem and aset of solutions from which to derive a refining solution that addressesthe problem, or the user might select a solution and a set of problemsfrom which to derive a refining problem that is motivated by thesolution. If the user acting on the DAG in FIG. 24 again refinessolution nodes 4 and 10, but this time while solving node 5, the DAG inFIG. 36 is a possible result.

In this model, there is no need to recognize any difference betweenkinds of nodes or between relations, other than to maintain thisinformation for and present it to the user.

Various issues discussed in sections below with regard to implicitaugmentation can also apply in the explicit scenario. Moreover, we willsee that with a tree-based view of the DAG, such as for example under “AMethod for Exploration of Hierarchical Structures and Representation ofContext Thereof”, these explicit operations can be performed entirelywithin the substructure, the context, or both, in a way that enablesenforcement of appropriate constraints.

FIG. 42 shows the hierarchical structure of an embodiment without regardto inheritance. The embodiment consists of a client system, a serversystem, and network connections between them. The client system runs abrowser that presents an interface through which users can explore oraugment a DAG. The client's augmentation process makes use of a generalroutine for augmenting a node, generating a proof and triggeringcommunication with the server. Underlying these is an operating system,which controls access to system hardware. The server system runs adatabase management system (DBMS) server and a web server. The webserver orchestrates between routines that build localized versions ofthe DAG with respect to a particular locus node or nodes for use by theclient and that modify the server's representation of the DAG. Theformer makes use of routines to reduce the server's full version of theDAG. The routines that modify the server's representation of the DAG andthat reduce the server's full version of the DAG access the databasethrough the database management system (DBMS) client. Various routinesmake use of the operating system, which controls access to systemhardware. The web browser (client) communicates with the web server viaHypertext Transfer Protocol (HTTP), which is transferred usingTransmission Control Protocol (TCP) and Internet Protocol (IP).

The user can be assumed to be particularly concerned with the entityrepresented by the node to which they navigated. It is useful to reducethe size of the DAG for various reasons. These include: to present onlythe most relevant information, to reduce the cost of transferringinformation to a separate machine on which the exploration andaugmentation are likely to take place, and to reduce the size of thegraph on which subsequent processing may take place. Also, in performingthis operation, the DAG is naturally segmented into the locus node, itscontext and its substructure, thus at any point in exploration can bepresented as a pair of trees. We will see that this representation isalso useful for the augmentation operation. It is possible, however, forembodiments to avoid reducing the DAG. Such embodiments still allow fornavigating through a DAG and may have equivalent notions of context andsubstructure based on following arcs to and from the locus.

Given a DAG Dag, for any entity E we define the DAG Dag_(E) ¹ to differfrom Dag only in that Dag_(E) ¹ excludes any nodes neither reachablefrom E in Dag, nor from which E is reachable in Dag.

FIG. 25 shows the DAG Dag from FIG. 24 after reduction with navigationcentered at node 1, i.e., Dag₁ ¹, while FIG. 32 shows Dag afterreduction with navigation centered at node 5, i.e., Dag₅ ¹.

Obtain Dag_(E) ¹ from Dag by including the locus node, and scanning andincluding its ancestors and descendants. With many-to-many relations, itis necessary to maintain a data structure of visited nodes to avoidincluding any common descendants multiple times, as is familiar to thoseskilled in the art of computer algorithms. FIG. 43 presents thisroutine.

Rather than necessarily processing the entire DAG, which could be quitelarge, especially if auxiliary information is being collected at thesame time, embodiments may place limits based on depth, cumulativestorage required, or any other mechanism. When the user indicates a needto proceed deeper into the hierarchy (requesting either moresubstructure or more context from any node at which construction of thelocalized DAG has been suspended), additional nodes could be fetched bythe server. In the localized DAG structure passed to the client, signalvalues could be inserted in place of the list of children of eachlogical tree (refining and related dependent entities in thesubstructure and refined and related independent entities in thecontext) having been deferred or, alternatively, dangling references canbe left in the localized DAG for entities whose information has not yetbeen retrieved from the server.

This can be implemented by having the server, when a limit has beenreached, store a continuation with each node at which scanning of theDAG is paused and associating that continuation with a URL through whichthe client can resume scanning that portion of the DAG. Manyembodiments, however, rather than maintaining such continuations byuser, may prefer to resume scanning of the DAG by having the clientprovide values for the free variables of the continuation, likelyincluding the entity at which scanning was paused. With this approach,in order to prevent the server from having to fetch all descendants,including those already residing in the client's localized DAG, theclient would need to pass that information with its request foradditional information.

Rather than fixing a depth limit across the application, embodiments mayallow it to be set in the parameters sent by the client requestinginitial access to entity information.

If a refinement relation is many-to-many, some embodiments may wish toprevent situations in which a direct refinement association is createdwhere an indirect one already existed, by checking for indirectrefinement between the various proposed parents of a refining entity.Other embodiments may leave these in place, on the basis that preventingthem requires checking for preexisting refinement upon creating newrefinement associations, a potentially expensive operation (especiallyif a depth-limit is placed on the DAG during localization as describedearlier in this section as “embodiments may place limits based ondepth”).

Alternatively, it is possible to allow these redundant associations tobe formed, but identify and remove them later, in a separate pass or,for example, during Reduce DAG 0210. We want to identify and eliminaterefinement paths of length one where a longer refinement path existsbetween the same entities. It suffices to keep, cumulatively, anassociation list or hash table as we descend through refinementsubstructure, mapping each sibling of the refining node beinginvestigated to its comprising refinement association. If an entity inthe dictionary is encountered, we can safely remove the correspondingassociation as redundant. Of course, a similar procedure could beapplied when scanning the context. A standalone version is presented inFIG. 44.

Multiple Simultaneous Refinement

We begin with the implementation of examples such as those of FIG. 24and FIG. 29 presented above under “Explicit DAG Augmentation bySpecialization”. The user again navigates to a particular node, selectsnodes from the resulting substructure or context (although someembodiments may restrict this selection to the proper substructure),and, if possible, is given the opportunity to define a new node (andentity) with the selected nodes (entities) as refinement parents. Again,the precise constraints on the node selection may depend on choices madeby the embodiment, but the selected nodes are assumed to be of the samekind, and the same kind as the intended child. We assume below forconcreteness that the operation is initiated from one of these intendedparents (the parentNode), but the selection can be initiated in anymanner.

There are often good reasons to associate with each dependent entity adistinguished independent entity, such as the problem addressed by asolution or the solution addressed by a supporting or opposing argument.Doing so implies that the derived relations such as addresses, supports,or opposes are many-to-one, such that, for example, a problem have manyproposed solutions, but each solution addresses only one problem.

If a refinement relation (take for example, directlyRefinesSolution) ismany-to-many (thus supporting multiple inheritance), then a cross-kindrelation for which that is the dependent kind (take for example,addresses) may be many-to-many, even if the given relation from which itis generated (directlyAddresses) is many-to-one, since the refinedsolutions may directly address different problems, all of which must beaddressed by the refining solution.

So an additional concern arises where the given (directly specified)cross-kind relation is many-to-one and we wish to assign to eachdependent entity a distinguished independent entity related to it by thederived cross-kind relation (as in, for example, addresses, motivatedBy, supports, and opposes, described above under “Project ManagementEntities and Relationships Including Separation of Problem and SolutionSpaces”). In particular, for dependent entities that are not otherwiseassigned such an independent entity through a direct cross-kindassociation and that refine dependent entities with such an assignment,there are various options of independent entity.

But there is also good reason to limit those options with acorrespondence constraint (see “Leveraging inheritance and tree view forsingle cross-kind augmentation with multiple simultaneous refinement”below as “to avoid inconsistencies with inheritance” and advantages incalculating GLB below in this section). In assigning an independententity to a new dependent entity under a cross-kind relation where thedependent entity refines one or more existing dependent entities,embodiments may require that for each refined dependent entity, somerefinement ancestor of the independent entity is directly related by thesame cross-kind relation to (has as a direct object) a refinementancestor of that dependent entity, indicating a correspondence betweenthe new cross-kind association and some preexisting, refined one (forexample, a refined solution addressing a refined problem). Someembodiments may loosen this constraint to require only that for eachrefined dependent entity, some ancestor (not necessarily refinement) ofthe independent entity is directly related by the same cross-kindrelation to (has as a direct object) an ancestor (not necessarilyrefinement) of that dependent entity. To take into account thismodification, the routines described below for validating proofs thatthe constraints hold would in some cases check that arbitrary paths areprovided rather than requiring refinement paths. Other embodiments maygo further and require only that each refined dependent entity share anancestor with the independent entity.

The user, in having navigated to a node of interest (perhaps an ancestorof the dependent entity nodes being refined) and having exploredthrough, for example, the substructure to those nodes, may have left thecurrent substructure or even context trees as an efficiently traversableguide to their intent. Embodiments can benefit from this record informulating policies for assigning independent nodes to new dependentnodes. The alternative to doing so is to search the substructure as asubDAG for common descendants or the context as a subDAG for commonancestors. But in addition to being inefficient this is unsatisfyingsince such common ancestors may not exist at all or there may be severalto choose from. Using trees at least provides sure access to commonancestors in the substructure tree and common descendants in the contexttree, although not vice versa, and not necessarily all via the necessaryrefinement ancestors and descendants. Common ancestors of distinct locusnodes may be made explicit in the context through the techniquespresented under “Presentation of Common Context of Multiple InvertedTrees”, and common descendants of distinct locus nodes in thesubstructure through the techniques presented under “Presentation ofCommon Substructure of Multiple Trees”. Ancestors may thus be locatedeither in the substructure or in the context for purposes of satisfyingthe correspondence constraints of the previous paragraph.

We would like for dependent entities to apply as generally as possible,e.g., we wish to associate each with an independent entity that is asgeneral as possible. Thus, embodiments may be tempted to associate withthe refining dependent entity a single most refining independent entitythat is refined by the independent entity assigned to each refineddependent entity, i.e., with a least upper bound (LUB) of the objects ofthe refined dependent entities with respect to the user's navigation.Indeed, solutions, for example, do relate, to some extent, to anyrefinement ancestor of a problem that they address.

Consider, for example, the DAG in FIG. 24. After the user navigates tonode 1, the DAG is reduced to that of FIG. 25. FIG. 27 shows the userexploring to nodes 4 and 10. If the user then refines nodes 4 and 10with a new node 13, as in FIG. 28, the resulting global DAG will forthis embodiment be as in FIG. 29. If distinguished independent entitiesare being assigned (see above in this section as “assign to eachdependent entity a distinguished independent entity related to it by thederived cross-kind relation”) as in the previous paragraph, node 1 isassigned to the new node 13, as the least upper bound of nodes 3 and 1.If instead, nodes 4 and 8 were refined, 2 would be assigned to the newnode as the least upper bound of nodes 3 and 6.

Embodiments assigning the LUB of refined nodes to the new refining nodemay have difficulty leveraging the knowledge of the user's focus on thelocus node in deciding what independent entity to assign to newdependent entities. Where the objects of refined nodes appear in thecontext, if they wish to favor the locus node, doing so effectivelyassigns to the new refining node the GLB of the locus node and the LUBof the objects of the refined nodes.

The natural alternative of a greatest lower bound (GLB) may provide abetter match to the refining dependent entity, and thus may be preferredby some embodiments. Calculation of LUB will thus be deferred todiscussion of generalization. For example, we might desire that everysolution be associated with a distinguished problem that refines anyproblem that it solves, or that every argument support or oppose adistinguished object that refines any object that it addresses.Unfortunately, as indicated above in this section as “search thesubstructure as a subDAG for common descendants”, the substructure treeprovides quite limited access to greatest lower bounds. Incorporatinginheritance may provide a more general solution.

Using the GLB to set the indirect objects of dependent entities alsoleads to a more natural decision corresponding to that presented abovein this section, i.e., whether or not to broaden the GLB inputs toinclude the locus node (assuming that it refines all of the objects, inthe context, of nodes being refined). If the locus node is a dependentnode, it is also possible to broaden the GLB inputs to include theobject of the locus node. Doing either would recognize the significanceof the user's having navigated to the locus as a signal of relevance.

The greatest lower bound mentioned above for assignment of independententities to dependent entities can be achieved (for example, in the caseof directlyRefinesSolution) by selecting the most specific problem fromamong the problems related to the solution by addresses, if a unique oneexists (i.e., one problem related to the solution by addresses, thatstrictly refines any other such problem) or by creating one, if therefinement relation on the kind yielded by the cross-kind relation(directlyRefinesProblem) is many-to-many (by automatically deriving acommon descendant problem and letting the refining solution directlyaddress that). Naive embodiments may check for refinement in eitherdirection among the various independent entities associated with thedependent entities to be refined, which may be considered inefficient.Other embodiments may cut this cost somewhat by allowing the user toselect or create the problem and having the system verify that it doesin fact refine the other addressed problems, at the cost of forcing theuser to deal with this complexity. Techniques presented here may reducethat cost.

We proceed to describe calculation of the independent node to relate tothe new refining dependent node as the GLB with respect to thesubstructure and context trees. In the case that no dependent nodesbeing refined were selected from the substructure (all were from theproper context), embodiments that enforce the correspondence constraintpresented earlier in this section can safely assign the object of theirLUB (in the inverted context tree, obtained using Calculate LUB wrt aTree 0101), if that LUB exists, to the new refining node, otherwisefail. Preferred embodiments, though, may skip this step and simply usethe locus node, as described above in this section as “broaden the GLBinputs . . . ”. Or in the case that any dependent nodes being refinedwere selected from the substructure, if they have a GLB in thesubstructure tree, embodiments that enforce the correspondenceconstraint can safely assign the object of the GLB to the new refiningnode. In the case that the dependent nodes being refined have the sameobject, embodiments may assign that object to the new refining node(this step may improve efficiency but can be omitted as it is covered bywhat follows). Otherwise (or for embodiments that prefer to go directlyto this approach), they may rely on the presence of the objects of thedependent nodes being refined in the substructure or context trees andcheck for a GLB among them, using Calculate GLB wrt Substructure andContext Trees 1111. Calculate GLB of Objects of Refined Nodes wrtSubstructure and Context Trees Explicit 3121 is in FIG. 46. Embodimentsmight instead check whether all refined nodes are in the context andreverse the branches; doing so is correct but slightly less efficient inthe case that only the locus and nodes from the proper context arerefined.

Calculate GLB wrt Substructure and Context Trees 1111 assumes that itsinputs arrive in a node list and first confirms that all members are ineither the substructure or the context, failing otherwise. Where anynodes are in the substructure, the client calculates the GLB of thosewith respect to the substructure tree, using Calculate GLB wrt a Tree0111, and ignores those in the proper context. Where all nodes are inthe context tree (and we haven't reverted to using the locus), it takestheir LUB with respect to the inverted context tree using Calculate LUBwrt a Tree 0101. Some embodiments might, in place of failing immediatelywhere indicated above, attempt to find the GLB in the DAGs by othermeans, such as a more exhaustive search.

We now present the underlying routines that calculate LUB or GLB withrespect to a single tree (substructure or context). In each case, weconsider only refinement paths! The LUB can be achieved by consideringthe refinement paths towards the locus node from each node (left toright), and taking the entity represented by the leftmost node of thecommon suffix of these paths. This algorithm is presented in FIG. 48.The GLB can be achieved by considering the refinement paths towards thelocus node from each node (left to right), and checking that all thesepaths are suffixes of a single, longest such path—the greatest lowerbound is the leftmost node of that longest path. This algorithm ispresented in FIG. 49.

The independent node that would be assigned to new node 13 under GLB inthe example of FIG. 24 and FIG. 29 presented above under “Explicit DAGAugmentation by Specialization” is 3.

While clients using this algorithm may obtain reasonable assignments ofindependent entities to dependent entities, the server may not wish totrust that all clients are playing by these rules (some may useunsupported code), and so may desire verification, for example that theobject of each entity being specialized is itself specialized by theprovided object of the new node (for now the purported GLB of all suchobjects), i.e., that the object of the new node is at least a lowerbound of the objects of the refined nodes. Such checks for chains ofrefinement associations can, however, be considered inefficient. Theserver may thus require assistance in the form of, for each dependententity to be specialized, a chain of entities related by refinement (weassume for concreteness from most specific to least) from the object ofthe new node to the object of that dependent entity being specialized,before establishing each association from the new refining entity to theexisting refined one. Of course, the order of the sequence is byconvention. Such a chain can be provided using the tree-based expositionof project structure. For each node being refined, the client can buildthe path based on one of several cases. For both the GLB and the objectof the node being refined in the substructure, the client traces thepath upward through the substructure tree from the GLB, followingrefinements until a node is reached with the object of the entity at thenode being refined. For the GLB in the substructure and the object ofthe node being refined in the context, we can take the path mentionedall the way to the locus and then concatenate the reverse of the pathstarting at the object node and ascending through the inverted contexttree to the locus. Embodiments that do not implicitly include the locusnode in GLB calculations (as described above in this section as “broadenthe GLB inputs . . . ”) may add a case for the GLB (and the object node)in the context and in that case use the reverse of the path obtained bystarting with the object node and ascending though the inverted contexttree until reaching the GLB. An embodiment of the proof generationprocess without this additional case is presented in FIG. 50, usingGenerate Proof Path 0113 from FIG. 59. In our example, if the userrefines nodes 4 and 10, the proof for this embodiment will consist, for4, of an empty path from the GLB, 3, to itself, object of 4; and for 10,of the path [2, 1] from the GLB, 3, to 1, object of 10. Note that byconvention we treat the initial nodes (3 and 1, respectively) asimplicit and do not include them in the paths. The client may be unableto build a correct validation depending on the current state of thesubstructure and context trees.

Putting these pieces together, the client can use Atomic ExplicitSpecializing DAG Augmentation 1141 to generate a single new node as arefinement of existing nodes. FIG. 45 describes the sequence forsituations where each dependent entity is assigned an object independententity as GLB with respect to the substructure and context of theobjects of the nodes being refined. First, for each node being refined,identify sequences of nodes related by refinement from its objectthrough the substructure or context, towards the locus node (embodimentsimplicitly including the locus node in the GLB can restrict themselvesto the substructure). This can be done using the current substructure orcontext trees, or any paths saved from prior substructure or contexttrees. It is also possible to generate a path using the localsubstructure or context DAG, but more than one such path may bepossible. Then, calculate the GLB of the objects of the refined nodes asin FIG. 46. In the case that the GLB does not exist, fail and provide anerror message. Use the GLB and its refinement path in generating theproof for the server as in FIG. 50. Meanwhile, prompt the user forinformation to be stored with the new entity. Then access the server torequest the augmentation operation, sending the proof. If it fails,clean up the partially-created node. Otherwise, update the clientinformation to include the new entity (creating a record for the newentity including the user-entered data and its object, and updatingrecords for entities of the nodes being refined to include the newentity as an additional child). The server returns the databaseidentifier of the new entity, which can be used by the client, forexample to build a URL for the new node.

The proof validation process where every dependent entity is assigned anobject (Validate Proof for Specializing DAG Augmentation with IndirectObjects 3211) is as in FIG. 51. The server may confirm that for eachentity being refined, the given path is in fact a chain of refinements,beginning with the provided object of the new refining entity (generallythe GLB of objects of the refined entities), and ending with an objectof the entity being refined. It follows the path provided through theglobal DAG, verifying that each step is a refinement.

Even if only direct objects are stored with dependent entities, theclient may sometimes be able to access an indirect object if it is inthe substructure above each refined node, or with a bit more effort ifit is in the context. While it may generally not be necessary tocalculate the GLB of the objects of the refined nodes, the initial stepof deriving paths from those objects, relevant for generating proofs,can then still be accomplished by following the path from each refinednode to the locus in search of a direct object. Proofs, in this moregeneral case, may need to identify both the chain of independententities, as before, but also the chain of dependent entities leading tothe one whose parent is the independent entity (the direct object). Theproof generation process for this situation, Generate Proof for ExplicitSpecializing DAG Augmentation with Direct Objects Only 1151, is as inFIG. 52. The proof validation process for this situation, Validate Prooffor Specializing DAG Augmentation with Direct Objects Only 3221, is asin FIG. 53. The server may confirm for each entity being refined, thatthe given independent path is in fact a chain of refinements, beginningwith the provided object of the new refining entity (generally the GLBof objects of the refined entities), and ending with a purported directobject of the entity being refined, that the given dependent path is infact a chain of refinements, beginning with the new refining entity andending with the refined entity, and finally that the purported directobject of the refined entity is genuine.

Where a distinguished independent entity is assigned to each dependententity, it is reasonable to store a reference to that assigned entitywith the dependent entity (or a filler in cases where we choose to inferthe assigned independent entity for refinements as described below under“Explicit DAG Augmentation by Specialization/Single cross-kindaugmentation with multiple simultaneous refinement”), so that cross-kindassociations need not be represented directly. Otherwise, it may bedesirable to directly represent such associations as a pair of entities.In either case, embodiments may choose to record not only the referenceto the independent entity, but evidence of the correspondence with arefined association, in the same form as the proofs described above (andbelow). The advantage would be to enable dissolving the cross-kindassociation between the refining entities if the refinement associationof dependent entities is dissolved.

Single Cross-Kind Augmentation with Multiple Simultaneous Refinement

We now turn to implementation of examples such as those of FIG. 24 andFIG. 36 presented above under “Explicit DAG Augmentation bySpecialization”. The user navigates to a particular node, selects nodesfrom the resulting substructure or context, and initiates a cross-kindoperation from a distinct parent node (the base node). If possible, theuser is given the opportunity to define a new node (and entity) with theselected nodes (entities) as refinement parents, and the entity at thebase node as a parent (independent entity) under the relevant relation.The precise constraints on the node selection may depend on choices madeby the embodiment as indicated below. Generally, we assume that theselected nodes are of the same kind, and the same kind as the intendedchild, or at least that the kinds are consistent. Embodiments,especially those that implicitly include the locus node in GLBcalculations (as described above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” as “broaden the GLBinputs . . . ”), may require the base node to be in the substructure andthe selected refinement parents to be in the proper substructure.

Now, for embodiments that assign an independent entity to each dependententity, rather than making this choice for ourselves we have the benefitof a directive from the user. But many embodiments may still want toimpose the correspondence constraint above under “Explicit DAGAugmentation by Specialization/Multiple simultaneous refinement”.

We now wish to demonstrate a path from the object of the new node (notnecessarily the GLB) to the object of each refined node. Severalquestions arise regarding the connection between the GLB of the refinednode objects of the nodes being refined and the independent node beingaugmented (the base node). If the base node refines the GLB of therefined node objects, we are guaranteed a path from the base node to theobject of each refined node, satisfying the correspondence constraint,and conversely without such evidence we are in danger of violating thatconstraint. And if the base node is refined by but not equal to the GLBof the refined node objects, we cannot set the new object to point tothe base without creating a situation where the refinements actually runin the opposite direction of that required. An example can help to makethis point more clear. FIG. 54 represents a DAG with navigation atproblem node 51. If a user were to solve its child problem node 52 witha new solution node 55 that specializes solution node 54, where 52 isparent of 53, the trivial GLB of objects of refined nodes 54, thesituation would be as in FIG. 55. Flattening the trapezoid into arectangle, it's easy to see that the two refinements run in oppositedirections. For some purposes, however, this contravariant relationshipmay be desired in place of the covariant one. Embodiments enforcing thecovariant constraint may choose, in the case that the base node cannotbe seen to refine the GLB of the refined node objects, either to ignorethe specified base node and treat this situation as a simple refinementor to consider this to be a user error. Other embodiments may allow theoperation regardless. To enforce the constraint, the GLB calculation canbe performed as before, but the result compared against the base node.

A routine to identify a path between two nodes in substructure orcontext is in FIG. 59. Note that we refer here to a sought path betweena refiningNode and a refinedNode; these names here have no relation toany other usage, in particular the nodes being specialized orgeneralized by the user. If the refiningNode is in the proper contextand the refinedNode in the proper substructure, fail immediately. Ifboth the refiningNode and refinedNode are in the substructure, follow arefinement path from the refiningNode towards the locus, until reachingthe refinedNode. If the refinedNode is found, return the path, otherwisefail. If both the refiningNode and refinedNode are in the context,follow a reverse refinement path from the refinedNode towards the locus,until reaching the refiningNode. If the refiningNode is found, returnthe reverse of the path, otherwise fail. Finally, if the refinedNode isin the context and the refiningNode in the substructure, concatenate therefinement path from the refiningNode to the locus with the reverse ofthe reverse refinement path from the refinedPath to the locus, failingif either doesn't reach the locus. Note here that an embodiment couldavoid checking for the first case and require only that the refinedNodebe in the substructure for the second case and only that therefiningNode be in the context for the third case, letting the failureshappen in that processing. We present Generate Proof Path 0113 as asingle routine although some embodiments may make assumptions that canreduce the number of cases in some situations.

If the base node is the same as the GLB of the objects of the nodesbeing refined, it is redundant and embodiments may choose to considersuch augmentations as simple refinements.

Where every dependent entity is associated with an independent entityand the correspondence constraint is enforced, we can use the proofmechanism described above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement”. An optimization is nowavailable since there is now a distinction between the base node and theGLB (this is also the case with the implicit GLB with the locus entity).Because all refinement paths share a common prefix from the base node tothe GLB of the refined node objects, that prefix can be separated sothat it need only be generated and validated once. Then, to obtain apath from the base node to the object of the refined node we wouldconcatenate the prefix with the independent path. Generation of proofsof this form by Generate Proof for Explicit Cross-kind and SpecializingDAG Augmentation with Indirect Objects 1112, using Generate Proof Path0113, is shown in FIG. 57. Their validation by Validate Proof forCross-kind and Specializing DAG Augmentation with Indirect Objects 3212is shown in FIG. 60.

If instead directlyAddresses (in the example presented above under“Explicit DAG Augmentation by Specialization/Multiple simultaneousrefinement” as “If a refinement relation (take for example,directlyRefinesSolution) is many-to-many . . . ”) is many-to-many orembodiments are not interested in extending it to a many-to-oneaddresses, and thus do not assign an object to dependent entities asdescribed above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” as “assign to eachdependent entity a distinguished independent entity related to it by thederived cross-kind relation”, they might still want to distinguish asubset of the problems related via addresses that is sufficient to reachthe others via application of refinesProblem. Even withoutdistinguishing any independent entities, embodiments can allow such“respectful” associations to be specified, e.g., allow an association tobe formed under the cross-kind relation between a dependent entity (B)and an independent entity (A) such that (B) refines another dependententity associated with an independent entity that is refined by (A). Inparticular, they can allow an association via directlyAddresses toleverage off of another such association, such that the solution andproblem of the first refine those of the second, respectively. Likewise,they can allow an association via directlyMotivatedBy to leverage off ofanother such association, such that the problem and solution of thefirst refine those of the second, respectively. Moreover, they canrequire that any cross-kind relation only allow the dependent entity torefine another entity if some refinement ancestor of the dependententity is related to a refinement ancestor of the independent entity.The approach described using proofs may support such requirements in alimited form that considers objects of dependent nodes to be theindependent entity of the first cross-kind association encountered afterrefinement associations on the path towards the locus.

In this case another modification to the proof structure described aboveunder “Explicit DAG Augmentation by Specialization/Multiple simultaneousrefinement” is useful, in addition to that described above in thissection as “an optimization is now available”. The proofs now take theform of a prefix path from the base node to the GLB and, for eachdependent entity being refined, of two refinement paths: one from thedependent entity and one from the GLB, each terminating with entitiesthat are in turn associated by the same cross-kind relation. Calculationof the independent path again uses FIG. 59. For refined nodes in thesubstructure, the dependent path is just the refinement chain towardsthe locus node. The proof generation process is as in FIG. 58. For theexample of FIG. 24 and FIG. 36 presented above under “Explicit DAGAugmentation by Specialization”, the proof for some embodiments will betwo pairs of paths, one for each node being refined (if indirect objectsare available, only the independent (problem) paths need be provided).In each case here, following the solution refinement hierarchy from therefined solution node towards the locus node and stopping at the objectproblem yields the refined problem/solution pair corresponding to thenew refining problem/solution pair being created by the currentoperation. For node 4, the dependent path for this embodiment will beempty because it is directly associated with independent node 3 (with norefined solutions in between) and the independent path for thisembodiment will be [3] because only that one step is required to reachthe object of 4 from the object 5 of new node 16. For node 10, thedependent path for this embodiment will again be empty since it isdirectly associated with independent node 1 and the independent path forthis embodiment will be [6, 2, 1], since following these nodes from theobject 5 of new node 16 leads to the object, 1, of 10. Note that byconvention we treat the initial nodes as implicit and do not includethem in the paths.

The steps for handling a single cross-kind and specializing DAGaugmentation are similar to those of Atomic Explicit Specializing DAGAugmentation 1141 in FIG. 45. They differ in the use of the routinesabove that are intended to support cross-kind and specializingaugmentation, including Generate Proof for Explicit Cross-kind andSpecializing DAG Augmentation with Indirect Objects 1112, Generate Prooffor Explicit Cross-kind and Specializing DAG Augmentation with DirectObjects Only 1132, and Specializing Cross-kind DAG Augmentation 3202, aswell as in adding a step to convert to the corresponding refinementoperation (e.g., of the kind of the nodes being specialized) if the GLB(calculated with FIG. 46) is the same as the base node. Because of thatpotential conversion, we include Generate Proof for ExplicitSpecializing DAG Augmentation with Indirect Objects 1131 andSpecializing DAG Augmentation 3201 in potential steps. The routine ispresented in FIG. 56.

The proof validation process with only direct objects is as in FIG. 61.The server may confirm that for each entity being refined, theindependent path, beginning with the provided object of the new refiningentity leads to an object of the entity to which the dependent path,beginning with the entity being refined, leads.

We emphasize that while embodiments of any sort may require validationas specified above, others may perform validation by other means, oromit it entirely.

Note that as described above in this section as “if the GLB (calculatedwith FIG. 46) is the same as the base node”, some embodiments may onlyuse a formal refinement operation when the assigned independent entityis in fact the GLB. Thus, a refinement of dependent entities may beassociated with an independent entity that is based on (the GLB of) theassociations of the dependent entities being refined. We can chooseeither to store this independent entity with the dependent entity, or tocompute it as necessary. If it is stored explicitly, this information isimmediately available, but must under various embodiments be maintainedas independent entity nodes and refinement associations are added orremoved.

Leveraging Inheritance for Specialization

Embodiments can achieve many benefits from leveraging inheritance ofstructure rooted at a dependent node through a refinement chain ofindependent nodes. Such structure can be presented to the user where itis likely to be relevant. Not only can users view such inheritedstructure, they can augment it, and in doing so specialize it to theircurrent state of navigation.

FIG. 62 is a version of FIG. 42 for an embodiment that supportsinheritance. The client's augmentation process includes high-levelroutines (Client Specializing DAG Augmentation 2101 and ClientCross-kind and Specializing DAG Augmentation 2102) that orchestratecopying of inherited nodes as well as a routine that copies an inheritedpath through a node's ancestors. The server's initialization processintroduces a high-level routine Localize DAG 2200 that makes use ofReduce DAG 0210 and new routine Inherit Structure 2230, which in turnuses the new routines Collect Inheritance 2240 and Record Inheritance2250 to collect nodes to be inherited from the user's context and toincorporate those into the localized DAG, respectively.

Leveraging Inheritance for DAG Exploration

Some embodiments allow inherited dependent entities to appear in thesubstructure of a locus node. Inherited structures may in fact besubDAGs, and those inherited structures may connect via any associationswith native (non-inherited) nodes in the substructure. After suchinheritance, the resulting DAG may continue to be explored as a tree.

FIG. 63 presents the routine Localize DAG 2200. It first reduces the DAGusing Reduce DAG 0210 to include only certain nodes and theirsubstructure and context and then inherits structure from the contextusing Inherit Structure 2230.

A particular embodiment uses a further modification to the DAGs. Dag_(E)² differs from Dag_(E) ¹ only in including as children of E entitiesinherited by E, e.g., entities dependent upon an entity refined by E.

FIG. 26 shows the DAG Dag from FIG. 25 with structure including nodes 9,11, 12, and 15 inherited, i.e., Dag₁ ². FIG. 33 shows Dag from FIG. 32with structure including nodes 4, 7, 8, 9, 10, 11, 12, and 15 inherited,i.e., Dag₅ ². The link from 10 to 1 has been spliced out of FIG. 26, assuggested below at the end of this section.

We next consider obtaining Dag_(E) ² from Dag_(E) ¹. For the locus node,call Collect Inheritance 2240 and then Record Inheritance 2250 for eachinheritedEntity, setting parentId to the entityId. FIG. 64 presents thegeneral structure of this routine. For example, if the locus node is aproblem, we might collect and record solutions of problems refined bythe locus problem. Note that although Inherit Structure 2230 ispresented as working over all cross-kinds relations, embodiments maycreate a separate version for each relation over which inheritance is totake place.

Intuitively, Collect Inheritance 2240 should only collect forinheritance the most general (refined) inherited entities, as morespecific ones would be subsumed in the process of recording inheritabledescendants of those entities. Our initial implementations of CollectInheritance 2240 and Record Inheritance 2250 are based on this intuitiveapproach.

Collect Inheritance 2240 scans the refinement ancestors of an entity.This involves avoiding double-counting any common ancestors. Whilescanning, we collect inheritable entities as defined above under“Project Management Entities and Relationships Including Separation ofProblem and Solution Spaces” and maintain minimal roots from which theycan be reached. This involves checking whether each encounteredinheritable entity refines one that has already been collected, or viceversa. Note that as described, when an inherited entity is encompassedby another inherited entity (i.e., appears on the left side of arelation with the other inherited entity on the right side), thisalgorithm includes both (via the encompassing entity returned by CollectInheritance 2240). Some embodiments may choose to include only theencompassed entity in this case (by Collect Inheritance 2240 returningthis encompassed entity), as the encompassing inherited entities mayoften seem irrelevant. That can be accomplished by keeping leaves ratherthan roots of the inherited entities. The advantage of the originalmethodology is that it leaves a possibility of creating new alternativederivations from the refining entities. FIG. 65 presents this routine.Note that with certain constraints, we can replaceencompassed/encompassing entities above with refining/refined entities.

Record Inheritance 2250 involves incorporating the collected inheritedentities and their descendants into Dag_(E) ², but this process mustterminate for any descendants that were already in Dag_(E) ¹. RecordInheritance 2250 begins by adding the inherited node as a child of thereceiving entity. It has cases depending on whether inheritedEntity wasalready in Dag_(E) ² or is being encountered for the first time. Ifbeing encountered for the first time, we add it to Dag_(E) ² under itsparent, and recur on its children. Otherwise, we add this parent to theDag_(E) ² entry. As stated, this process may leave immediate descendantsof the locus node in place even if they are reachable from inheritednodes. Preferred embodiments may splice out such nodes, so that they arereachable only by the longer path via the inherited nodes. FIG. 66presents this routine.

In the case of skill requirements being inherited through solutionrefinement, Record Inheritance 2250 becomes trivial. This is because, asdescribed above under “Project Management Entities and RelationshipsIncluding Separation of Problem and Solution Spaces” as “the refinementrelation acts in the opposite direction in the inclusion for skillrequirements by a solution”, superskills rather than subskills of askill are necessarily required by refinements of solutions requiringthat skill. The tracing downward through subskills that would beperformed by Record Inheritance 2250 is thus not necessary. So, theskill to be inherited by a solution can simply be attached to thesolution as an orphan inherited node. There is little insight to begained by presenting a subskill hierarchy in the same DAG as a projecthierarchy.

Checks for whether or not nodes refine each other can be inefficient, soit is fortunate that the intuitive algorithm can be modified in severalways to avoid these checks. In each of these enhanced algorithms, we donot require Collect Inheritance 2240 to filter the most generalinherited entities, but rather have it return all entities that aredirectly inheritable. We do have it fix an ordering of such entities, sothat Record Inheritance 2250 can process them either most-general firstor most-specific first.

In FIG. 67 we show a version of Collect Inheritance 2240 that ensuresthat the sequence in which inheritables are listed is consistent withthe position of the node from which they were inherited on a refinementpath from the locus node, e.g., more specific preceding more general. Ina programming language with recursion, this could be implemented as apreorder tree traversal. We may thus be expecting Record Inheritance2250 to include inheritable descendants of these more shallowly locatedentities and then to include inheritable descendants of the more deeplylocated entities. It is possible that some of the former descendants maybe included among the latter. Such already-formed nodes should betreated just as any encountered nodes that were not inherited at all butpart of the original substructure. Thus, Record Inheritance 2250 maywork unchanged.

But we can do even better. By recording the inheritables in adeepest-first order (by reversing the output of the shallowest-firstversion of Collect Inheritance 2240 or by inserting the inheritedentities at the beginning of the list rather than the end (in FIG. 68)),embodiments may be able to avoid the Record Inheritance 2250 processaltogether in the case that the inheritable entity is already known, ifthey have already recorded a more incremental way of reaching it. Infact, various embodiments must check for that case so as to avoidcalling Record Inheritance 2250 on a more shallow entity that has beenadded to the subDAG in the process of recording a deeper one, generatingexcess links. Record Inheritance 2250 can then also be modified (as inFIG. 70) to wait until just before recurring on each child to check thepresence of nodes in the subDAG. In a language with recursion, thiscould also be implemented (in FIG. 69) as a postorder tree traversal,inserting elements at the end of the list as in FIG. 67.

For embodiments that are also scanning the context of the locus node togenerate a subDAG, another possible optimization may take advantage ofthis fact to collect inheritables at the same time.

For embodiments that include restating refinements, we prefer theshallowest-first versions because the restatement may be added to thesubDAG while giving an opportunity to avoid adding the restated entity.If the deeper entity were recorded first and it were restated by anotherinherited entity, the former would need to be removed from the subDAG.

Even when inheritables are recorded in preorder (without filtering forrefinements), if the cross-kind relation being inherited ismany-to-many, it may be possible for the same inheritable entity to bereachable by multiple refinement paths. In that case, the abovedescribed check may still work to prevent duplicate recording, but moreefficiently, embodiments may return the inheritables as a set (so thatwe prevent duplicates by checking membership prior to the insertion inCollect Inheritance 2240).

For some embodiments, it is not technically necessary to check whetherthe first inheritable entity being recorded is already in the subDAG (itwill not be). It should be clear to those skilled in the art of softwaredevelopment how to adjust the process to avoid this first check.

FIG. 27 and FIG. 37 show such trees for FIG. 26, the former exploringnodes 4 and 10, the latter exploring to nodes 12 and 15. FIG. 34 showssuch trees for FIG. 33 after exploring to nodes 4 and 8.

As described under “Explicit DAG Augmentation by Specialization” as“When the user indicates a need to proceed deeper into the hierarchy . .. , additional nodes could be fetched by the server”, some embodimentsmay wish to provide deferred access to portions of the DAG. Suchembodiments would likely merge the routines mentioned above into tworoutines, one for context and one for substructure, through a techniquesuch as deforestation, as is familiar to those skilled in the art ofsoftware engineering. In this case, not all inherited nodes would beimmediately available to the user. When a user attempts to explorefurther into the context from a refined ancestor of the locus for whichcollection of inheritance (and refined ancestors and related independentnodes) that has been deferred, the additional inherited nodes (bothdirectly inherited and their descendants) can be recorded in theclient's localized DAG much as the procedure described for the server inRecord Inheritance 2250. The user might also be provided with a “More”link as described below under “Aggregations of Auxiliary Information” as“embodiments may include a “More” link in the results” to indicate thatadditional inherited nodes are available and, if activated, to triggerloading of additional nodes and their inheritance into the local DAG.

Leveraging Inheritance and Tree View for DAG Augmentation

A user can augment DAGs representing project information. DAG (asopposed to tree) structure can be due to: many-to-many refinementrelations (multiple inheritance); a cross-kind relation where dependententity also refines one or more existing dependent entities; or across-kind relation that is many-to-many. Each of these have their ownchallenges and opportunities.

If the user has navigated to a node in the context of the nodes to beaugmented, the user may explicitly select those nodes in a manner notdissimilar to the explicit DAG augmentation described above. In othercases, it may be possible to leverage inheritance in the augmentationprocess.

Consider again the DAG in FIG. 24. After the user navigates to node 5,the DAG is localized to that of FIG. 33. FIG. 34 shows the userexploring to nodes 4 and 8. Nodes 4 and 7 are now inherited by node 5,with node 8 refining 7. If the user then refines nodes 4 and 8 with anew node 14, as in FIG. 35, the resulting global DAG for this embodimentwill be as in FIG. 36. The new node 14 for this embodiment will not onlyrefine nodes 4 and 8 but also implicitly be associated with the locusnode 5 through the cross-kind relation (such as solving the problem).Because 5 is the GLB of 3 (object of 4) and 6 (object of 8), embodimentsmay choose to consider this as a refinement. But if the user hadnavigated to a refinement descendant of node 5 and performed the sameoperation, it would clearly be recorded as a direct cross-kindassociation. Notice that merely by expressing an interest in the node 5,the user is given immediate access via inheritance to the nodes that canbe extended so as to relate to that node, and not restricted by factthat node 5 is the GLB of 3 and 6 only in the global DAG and not withrespect to any substructure tree.

Leveraging Inheritance and Tree View for Multiple SimultaneousRefinement

For some embodiments, multiple simultaneous refinement is indicated whenthe user selects nodes for refinement, not all of which are inheritedcross-kind associations of the same kind, but rather the inheritedcross-kind associations differ in kind or at least one node to berefined is part of the substructure. (We say “cross-kind association”here rather than simply “node” because multiple cross-kind relations mayshare the same dependent kind’.) We will see that if all of the nodesselected for refinement are inherited cross-kind associations of thesame kind, we prefer to treat the operation as a similar cross-kindaugmentation.

For now, we may assume that inherited nodes that do not refine adirectly inherited node may not be selected for refinement, but that maychange for embodiments that implement iterated augmentation.

Consider again the localized DAG with inherited nodes in FIG. 26. Ifnodes 4 and 10 are refined and distinguished independent entities arebeing assigned as described above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” as “The naturalalternative of a greatest lower bound (GLB)”, node 3 is now assigned tothe new node, as the greatest lower bound of nodes 3, and 1. Likewise,if nodes 8 (via 7) and 10 are refined and distinguished independententities are being assigned, node 6 is assigned to the new node, as thegreatest lower bound of nodes 6, and 1. If nodes 4 and 8 are refined,embodiments can fail, can search the substructure for a unique greatestlower bound, if a unique one exists (here node 5), create one if noneexist, or allow one to be selected if multiple exist. Failure is not abad option, since as described below, the user can accomplish thisaction by navigating to the node that they prefer to serve as the lowerbound.

Likewise, embodiments that implicitly include the locus node in GLBcalculations (as described above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” as “broaden the GLBinputs . . . ”) can, in the presence of inheritance, exclude objects ofany inherited nodes from that calculation, as the independent entitiesassigned to them will be refinement ancestors of the locus node, andthus refined by the independent nodes assigned to entities representedby the non-inherited nodes. Preferred embodiments may relate the locusnode to the refining dependent node if all refined entities areinherited (and they refine the directly inherited entities), but othersmay choose to include inherited nodes in the computation in that case,selecting a node in the context using the LUB algorithm above (since thecontext hierarchy is inverted).

Again, the server may wish to verify refinement operations requested bythe client where an indirect object is set for any new dependent entityby requiring, for each dependent entity to be refined, a chain ofentities related by refinement (we assume for concreteness from mostspecific to least) from the greatest lower bound to the object of thatdependent entity. We saw previously that such a chain can be generatedby the client using the tree-based exposition of project structure. Ifthe object of a refined node was in the context DAG, however, it had tobe revealed in the context tree in order to generate the necessaryrefinement chain. If the refined node is inherited, it can generate thenecessary refinement chain using a combination of the inheritancemechanism and the tree-based exposition of project structure as, fornoninherited nodes, the path from the greatest lower bound up throughthe substructure tree as long as it traces refinement associations,until it reaches the object of the node being refined, or for inheritednodes taking this path towards the locus node and then, if the pathreaches the locus, concatenating it with the path through the global DAGby which that node being refined was inherited. The modified proofgeneration process is as in FIG. 74, using Generate Single IndependentPath of Proof for Specializing DAG Augmentation 2113 from FIG. 76. Inour example involving FIG. 24 and FIG. 33 through FIG. 36, presentedabove under “Leveraging Inheritance and Tree View for DAG Augmentation”,if the user refines nodes 4 and 8, the proof for this embodiment willconsist, for 4, of the inheritance path [3]; and for 8, of theinheritance path [6] (the initial node 5 is here assumed by conventionto be implicit). If the user had navigated to node 1 and refined nodes 4and 11, the proof would consist, for 4, of the empty path (from the GLB,3 to itself, the object of 4); and for 11, of the path [2, 1, 0],obtained as the path from the GLB 3 through the substructure to 1followed by the inheritance path [0] (the initial node 3 is againassumed by convention to be implicit).

How can such inheritance path be procured by a client? It can be derivedby the server during Collect Inheritance 2240 and passed to the clientalong with the localized DAG, so that it can be tracked and ultimatelyproffered back to the server. We present a version of CollectInheritance 2240 that collects inheritance paths in FIG. 71. It differsfrom FIG. 68 in maintaining an inheritance path, which is extended uponencroaching further into the context and retracted upon retreating.

As an optimization, embodiments might choose not to work with a directmapping from directly inheritable entities to paths but rather with acomposition of mappings, first from directly inheritable entities to theindependent entities from which they are inherited, and second fromthose independent entities to paths from the locus.

The proof validation process is as in FIG. 51. The server may confirmthat for each entity being refined, the given path is in fact a chain ofrefinements, beginning with the provided object of the new refiningentity (generally the GLB of objects of the refined entities), andending with an object of the entity being refined.

Call a ‘flow’ a DAG with designated source and sink nodes. Anyrepresentation of a DAG or of a general graph available to those skilledin the art of software development would be acceptable for this purpose,although specialized representations are possible, including thatsuggested under “A Method for Exploration of Hierarchical Structures andRepresentation of Context Thereof”. Although only one inheritance pathis required to validate the augmentation, an enhancement would be toreplace the inheritance path sent to the client with an inheritanceflow, so that in the case where a node might have been inherited by anyone of several inheritance paths, the client could maintain and theserver receive proofs involving not just an arbitrary such path but theflow of such paths. The advantage would be that if various but not allsuch paths are disrupted by node deletion, the refinement operation mayhave optimal chance of succeeding.

This approach requires Collect Inheritance 2240 to return a flow witheach collected entity, not just a path. Store with each independent nodea map from inherited entities to flows by which they can be reached.Recur on each refined entity to obtain such a map (if not alreadyvisited), and then add the current node to the front of each flow ineach map (e.g., create a flow with a new start node that points to thestart node of the old flow). If an entity is reached more than once,each additional time don't recur further but on unwinding add adifferent new front node. After processing all refined entities, mergetheir respective maps (e.g., create a new map whose domain is the unionof the domains of the maps for each refined entity, and for any entitythat appears more than once, merge its flows). To merge flows with thesame start and end nodes using a standard graph representation, simplytake the union of the entity set and the union of the edges. Theapproach is presented in FIG. 72, still using inheritancePath to model astack. The optimization described above in this section as “embodimentsmight choose . . . to work . . . with a composition of mappings” applieshere as well. In Generate Single Independent Path of Proof forSpecializing DAG Augmentation 2113 from FIG. 76, the paths ofindependent nodes included in proofs could then either take the form ofa sequence of nodes (the path to the locus node) along with a possiblyempty flow representing the inheritance path, or these two elements maybe combined into a single flow. Validate Proof for Specializing DAGAugmentation with Indirect Objects 3211 from FIG. 51 is then easilymodified to try alternate paths instead of immediately failing if thefirst path through the given flow does not succeed.

Including inheritance, the steps for handling a single specializing DAGaugmentation are in FIG. 73. It differs from Atomic ExplicitSpecializing DAG Augmentation 1141, described above under “Explicit DAGAugmentation by Specialization/Multiple simultaneous refinement”, inusing the inheritance-aware versions of routines in figures FIG. 74 andFIG. 78 as described above. Embodiments implicitly including the locusnode in the GLB may avoid processing inherited refined nodes entirely,since their objects may be in the context. Where the locus node refineseach object of a refined node and all refined nodes are inherited, someembodiments may, along the lines of implicitly including the locus nodein GLB operations, convert the refinement operation to a cross-kindoperation with the locus node as the base node. We will see thatiterated copying or restatement of refined nodes may provide a morerobust solution.

For embodiments and entity kinds where only direct objects areavailable, the proof generation process (Generate Proof for SpecializingDAG Augmentation with Direct Objects Only 2121), modified from FIG. 52to use Generate Single Independent Path of Proof for Specializing DAGAugmentation 2113 of FIG. 76 to deal with inheritance, is in FIG. 75.

Leveraging Inheritance and Tree View for Single Cross-Kind Augmentationwith Multiple Simultaneous Refinement

Many embodiments leverage inheritance to reduce both the cognitive loadon the user and the system processing required to augment a DAG. If theuser navigates to the most refining independent node, making it thelocus, for some embodiments they will see as inherited nodes only thevarious dependent nodes that they might choose to select for refinement,such that the locus node represents the distinguished independent entityfor the newly created refining dependent entity.

More generally, for some embodiments, cross-kind augmentation isindicated when the user selects a node for such augmentation, or whenthey select nodes for refinement, all of which are inherited cross-kindassociations of the same kind. For cross-kind relations where thedependent entity also refines one or more existing dependent entities,there are several concerns.

The first is making it intuitive and natural to create suchassociations. We have seen that it can be appropriate to define adependent entity with respect to one or more existing dependententities, for example a solution with respect to one or more solutionsof refined problems or a problem with respect to one or more problemsmotivated by refined solutions, and that in these cases it is possibleto have the user manually select both the entity to extend and those torefine. Many embodiments rely, however, on the insight that suchassociations can be intuitively formulated by refining an inheriteddependent entity. This technique can extend to refinement not just of animmediately inherited node but of any inherited descendants of thatnode.

Simply refining any explicit selection of dependent nodes inherited bythe locus node, where the dependence relation is direct, could beinterpreted, because the user has navigated to a particular locus node,as creating a new dependent node that not only refines the entitiesrepresented by the selected inherited dependent nodes, but also forms adirect cross-kind association with the locus entity (as the independentnode).

This and the following section provide methodology for creating suchrefinements, which we also refer to as restatements. The section“In-place, Iterating DAG Augmentation” introduces variousimplementations and uses of restatements, any number of which can beapplied without introducing in-place, iterating DAG augmentation.

For refinement of inherited dependent entities, both the dependent andindependent paths trace refinement relations up through the substructuretree as long as they follow refinement associations. If the independentpath leads to the locus node, the inheritance path (or DAG) of thedependent node is concatenated onto the independent path. FIG. 78differs from FIG. 57 in using the inheritance-aware procedure GenerateSingle Independent Path of Proof for Specializing DAG Augmentation 2113from FIG. 76 in Generate Proof for Cross-kind and Specializing DAGAugmentation with Indirect Objects 2132. For the example involving FIG.24 and FIG. 33 through FIG. 36, presented under “Leveraging Inheritanceand Tree View for DAG Augmentation”, the proof for some embodiments willbe two pairs of paths, one for each node being refined. In each casehere, the client follows the solution refinement hierarchy from therefined solution node towards the locus node, and follows the problemrefinement hierarchy from the problem being solved (the locus node)through the path by which the solution was inherited. The independentpaths for this embodiment will be unchanged from those described aboveunder “Leveraging inheritance and tree view for multiple simultaneousrefinement” with respect to that example. For node 4, the dependent pathfor this embodiment will be empty, since it has a direct object. Fornode 8, the dependent path for this embodiment will be [7], a singletonof its refinement parent, which does have a direct object. Note that byconvention we again treat the initial nodes as implicit and do notinclude them in the paths.

Even if we do not require that each dependent entity be associated witha single refining independent entity, there is another reasonembodiments might choose to constrain the dependent nodes that can berefined along with augmenting an independent node. That is to avoidinconsistencies with inheritance. The operation of creating a dependententity related to an existing independent entity and also refiningexisting dependent entities can in general lead to a situation where theunion of various relations after inheritance may in fact be cyclic. Fora simple example, consider beginning with a solution addressing aproblem and introduce a problem that refines the problem being solvedwhile being motivated by the solution. More generally, we wish to avoidsituations where the refined entity is reachable by following object-ofassociations (from a cross-kind relation) from the refining entity. Forthe case of problems being objects of solutions which are in turnobjects of problems, those situations could only occur with an evennumber of applications of cross-kind relations. These are notnecessarily direct object associations, but may involve refinements aswell. The constraint above is sufficient to prevent such cycles, andembodiments may determine whether or not it also precludes projectstructures that they consider useful. These cycles, however, may not beconsidered problematic. The only irregularity would be that the sameentity might appear in both the context and substructure. Embodimentsmight arrange to collapse hierarchies as necessary to prevent more thanone node associated with the same entity from being visible at the sametime.

Again, putting these pieces together, the client can generate a singlenew node as a cross-kind augmentation of a base node while refiningother existing nodes. The routine, shown in FIG. 77, differs from thatpresented in FIG. 56 and described above under “Explicit DAGAugmentation by Specialization/Single cross-kind augmentation withmultiple simultaneous refinement” only in using the inheritance-awareversions of routines in FIG. 74 and FIG. 78 as described above in thisand the previous section. Again, embodiments implicitly including thelocus node in the GLB can avoid processing inherited refined nodesentirely, since their objects will be in the context.

From what has been presented so far, a user can perform augmentationoperations on inherited or noninherited nodes in the substructure of alocus node (inclusive of the locus), except that if the user specifiesan augmentation of an inherited node that is not and does not refine adirectly inherited node, embodiments may need to issue an error message.Such situations can be handled through the iteration of augmentationspresented in the next section.

Iterating DAG Augmentation

Where the dependence relation is indirect (a composition of variousdependent cross-kind associations and refinement associations), it ispossible to iterate the process demonstrated in the example involvingFIG. 24 and FIG. 33 through FIG. 36, presented under “LeveragingInheritance and Tree View for DAG Augmentation”, copying the inheritedstructure such that each new node maintains links to the previouslycreated node, and ultimately to the locus node. Any inherited structurethat is common to multiple inherited nodes should only be copied once.It is actually not necessary to recreate the entire structure; forexample, some embodiments may be content to recreate only the cross-kindassociations, eliding the refinement associations by considering thecross-kind associations to relate the most refining entities.

Given the DAG in FIG. 24, the user could perform a sequence ofoperations, first navigating to node 1 and refining node 9 to node 9′with respect to node 1, then navigating to the new node 9′ and refiningnode 15 to 15′ and 11 to 11′, each with respect to node 9′, navigatingto 11′ and refining 12 to 12′ with respect to 11′, and finallynavigating back to 9′ and refining 12′ and 15′ to 17′ with respect to11′. The DAG in FIG. 39 is a possible result. We show here how toautomate sequences such as this. Recall that FIG. 25, FIG. 26, and FIG.37 present various stages of processing to present the DAG localized atnode 1 as a tree through which the user can explore nodes 12 and 15.

Note that with this iteration, the user may select for augmentationinherited nodes, even those that are not and do not refine a directlyinherited node. This was a problem before because such nodes could notbe implicitly connected to the locus. Because preceding inherited nodeson the path to the locus will be copied in turn, the connection to thelocus is generated one augmentation at a time.

FIG. 38 shows the process of refining problem nodes 12 and 15 with a newproblem node (17) that addresses it with respect to node 1. FIG. 39,again, shows the full resulting DAG after this process.

In general, we will want the new entity to descend from both theinherited node being augmented and also ultimately from the node thatreceived that inheritance. As displayed in FIG. 38, embodiments maycreate a structure corresponding to and refining the inherited structureon any path from the locus down to the nodes being augmented. This mayinvolve replicating (but allowing the user to rename and otherwiseadjust) any inherited nodes on the path from the locus to the base nodebeing augmented by the cross-kind relation as well as any inheritednodes on the path from the locus to the nodes being refined, but takingcare to replicate any common nodes only once. After replicating theinherited structure, there may be an additional step of creating thefinal node to augment that refining structure.

Some embodiments (including the one we describe below) prompt the userto define the augmenting nodes in a top-down manner, starting with achild of the node receiving the inheritance. Other embodiments promptthe user to define the augmenting nodes in a bottom-up manner, startingwith the child of the inherited node being augmented.

When augmenting a node using a refinement relation, some embodiments maypresent the value of the refined node as a default initial value for therefining node, while other embodiments may not provide any such defaultinitial value in these cases.

Some embodiments (including the one we describe below) allow the user torefine each inherited ancestor of the inherited node. Other embodimentsprefer to not refine every such inherited ancestor of the inherited nodebeing augmented, but rather, in any chain of refinements among thoseancestors, only refine the final refining ancestor and consider that todirectly participate in the next association with a node of differentkind (for example either a solution addressing a problem or a problemmotivated by a solution).

Embodiments might, as described below in this section as “the inheritedstructure being augmented”, allow operations to be performed directly oninherited nodes, but before such operations are performed, request ofthe user new information, for the ancestors of each inherited argument,in order to copy and modify them to recognize their position under thelocus node. Alternatively, embodiments might only support restatement ofinherited nodes and not other operations, so that the user has no choicebut to explicitly restate each argument before proceeding.

Note that although an arbitrarily complex DAG structure may be inheritedby the locus entity and integrated with its descendants, as the userexplores the substructure from the locus node to arrive at an inheritednode to augment, for various embodiments there will be a distinguishedpath back to the locus node, retracing those steps, as the substructurenodes form a tree rooted at the locus node.

Note also that we can (but need not) assume that the first inheritednode is of a different type than its parent, because, for example, aproblem is inherited through a chain of refinements of solutions and asolution is inherited through a chain of refinements of problems.

Now we can present a high-level process flow that incorporates thisiteration for an explicit refinement operation. We begin by initializinga data structure to hold the results of copying inherited nodes. It maybe used to avoid copying any node more than once. The implementationtreats the parent node (from which the refinement is initiated) as justanother refined node (distinguished here only by its use in locating thefinal augmentation) rather than a base node for a cross-kindaugmentation. Data structures are also initialized for collecting thenew nodes and paths through new nodes (if not already in place), whichwe next generate by calling Copy Inheritance for Specialization 2103 oneach refined node and store in said structures. Prior to calling CopyInheritance for Specialization 2103 on each refined node, we generatethe path from that node to the locus (if not already in place) for usein that routine. After replicating the inherited structure beingaugmented, we can proceed by prompting the user for informationregarding the explicitly augmenting node and create it using AtomicSpecializing DAG Augmentation 2141. Embodiments may differ on whether anexplicit refinement of a single node is handled via the copying processfor that node, or with the explicit augmentation after the implicitcopying has completed. The former option, outlined in FIG. 80, qualifiesthe final augmentation to ensure that it is not a refinement of a singleinherited node. The latter option, consistent with the approach of onlycopying the last refining inherited node as described above in thissection as “only refine the final refining ancestor” and outlined inFIG. 81, instead qualifies the copying of inherited refined nodes toavoid the case of a single node. Still other embodiments may perform therefinement twice, and indeed this may be the preferred approach foriterating in-place, as described below under “In-place, Iterating DAGAugmentation”.

The process for a cross-kind (and refining) augmentation is outlined inFIG. 82. It differs from FIG. 80 and FIG. 81 in omitting the step oftreating the parentNode as refined, in not having to deal with the issueof single refinement, in copying inherited ancestors of the base node aswell as inherited ancestors of refined nodes, and, of course, in theform of the final augmentation (using Atomic Cross-kind and SpecializingDAG Augmentation 2142).

FIG. 84 presents a trace of the routine for the example of FIG. 38.

The process of augmenting inherited nodes may involve copying theinheritance ancestry structure of each of those nodes. The routine CopyInheritance for Specialization 2103 is responsible for iterativelyregenerating the inherited ancestors of a single inherited node beingaugmented (either a base node or a node being refined). The result is apointer to the new node (which in turn points to its parents) and, forembodiments in which the server requires validation on augmentations, apath from the node being augmented towards the locus that can be usedfor generating those proofs. This routine is displayed in FIG. 83. Weassume a stack in this description. The content of each stack entry maybe assumed to include an inherited node and the operation by which itwas derived. Under embodiments in which the operation can be inferredfrom the kind of node, holding only the inherited node may suffice.Along with or incorporated within the inherited node is a way ofreaching the parents of that node. The stack may be implementedexplicitly as such, the system stack may be used (pushing by passingparameters to procedures, popping by returning), by building up acontinuation that processes the value being pushed around any previouslybuilt-up continuation, or by any other computational process known bythose skilled in the art to implement a stack. The routine is composedof two loops performed in sequence: the first descending throughancestors while building up the stack and the latter feeding off of thestack while copying inherited nodes. For the first loop, scan upwardthrough the ancestors of the node being augmented, pushing eachinherited node encountered, until either a node already copied or anon-inherited ancestor is reached. In the former case, begin the secondloop with the stored values. In the latter case, use the noninheritedancestor as the newParentNode and prepend parentPath with inheritedNodefor newPath in beginning the second loop. For various embodiments, thisfirst such copied node (copy of the last inherited node) will alwaystake the form of a cross-kind augmentation of newParentNode (the parentof inheritedNode) as in Atomic Cross-kind and Specializing DAGAugmentation 2142, since the node was inherited as a cross-kindassociation. Otherwise, embodiments may push inheritedNode andparentPath for later use and proceed through the ancestor hierarchy bysetting inheritedNode to its parent and replacing parentPath with aversion without the first element to continue iterating through thefirst loop. After, copying the last inherited node as newNode,embodiments may build finalPath (for use in proof generation) byprepending newNode to newPath. At this point, they may record newNodeand finalPath in the data structure of already copied nodes and ensurethat newNode is situated under inheritedNode and parentPath, so that GLBcalculations may proceed without error. Finally, embodiments canformally begin the second loop by checking whether the stack is empty,which is where they would pick up if using precomputed values. If so,they may be done; otherwise, they may both pop the stack to obtain thenext-shallowest inherited ancestor node and parentPath and setnewParentNode to the copy of the next-deepest ancestor. At this point,embodiments may copy inheritedNode. If inheritedNode is a cross-kindaugmentation of its parent, embodiments may proceed as above with AtomicCross-kind and Specializing DAG Augmentation 2142. But if inheritedNodeis a refinement of its parent, they may instead use Atomic SpecializingDAG Augmentation 2141 with inheritedNode and newParentNode as therefinedNodes and proceed as after the corresponding node creation step.

We note that to the extent that all nodes are in fact copied, we cansimplify the matter of refining inherited nodes described above withrespect to a many-to-many refinement relation. Since we are copying eachof the dependent nodes to be refined, for various embodiments theultimate multiple refinement will refine these “copies”, each of whichis associated not with the independent node associated with theinherited dependent node, but with the locus node. It should thus bepossible in this case to require that for any multiple refinement ofdependent entities, that they be associated with the same independententity. An intermediate step would be to require that one such dependententity to be refined, say the last, be associated with an independententity that refines the independent entities associated with the otherdependent entities to be refined.

Embodiments needing to automate augmentation of the DAG by extending thelogical substructure tree may on occasion find that the desired DAG nodemay not be visible because a different section of the DAG may have beenexpanded. This can be handled by rearranging the display to reveal thedesired node. Procedures to do that for the nodes in the substructure isin FIG. 213. It accepts a path and operates by first scanning throughthe already-visible portion of the path and upon not finding a requirednode, first closes any conflicting siblings and then begins unfoldingthe path, one node at a time.

The description of Copy Inheritance for Specialization 2103 above inthis section is limited in that it assumes that the path from the nodebeing augmented (or otherwise acted upon) to the locus node will beentirely made up of inherited nodes (excepting the locus node). It ispossible that the logical substructure tree may pass between inheritedand non-inherited nodes. Such a situation could come about if a diamondis inherited and one path through it is copied but the user thenexplores through the other path. There will, however, always be a pathin the local DAG from any inherited node to each locus node throughwhich it was inherited, so some embodiments may deem that sufficient.For others, Copy Inheritance for Specialization 2103 could be modifiedas follows to work in such a scenario. Rather than just turning backupon any noninherited node or node that has already been copied, theymight turn around only for a locus node or node that has already beencopied. As embodiments return back down the path from the locus node, asthey reach a first non-inherited node after an inherited node, ratherthan creating a node and associating it with the copied parent entity,they may instead create an association between that entity and the onethey are tracking on the path, passing their own node down to the nextnode on the path to be linked with in case it is inherited. Anysubsequent noninherited nodes would simply replace the parent node withtheir own node as they return to the child, in case the child isinherited. FIG. 85 modifies FIG. 84 under the pretense that nodes 11+and 12+ are not inherited. As an optimization, embodiments mightdetermine as they ascend the path which nodes require a node to bereturned and even which need to be copied, limiting the work required onthe return trip.

In-Place, Iterating DAG Augmentation

This iteration can be made more intuitive in the case where thecross-kind relation is many-to-one. Rather than creating a parallelstructure corresponding to the inherited one, we can modify theinherited structure in-place. This may seem odd at first because astructure that appears lower than another in the hierarchy many notactually be below it in the global DAG (if only the latter wereinherited). It can, however, once this is accepted, provide a conciseand intuitive representation.

Given the DAG in FIG. 24, the user could perform the sequence ofoperations described above with respect to the example involving FIG. 24and FIG. 39 under “Iterating DAG Augmentation” in-place. The DAG in FIG.41 is a possible result. It differs from FIG. 39 only in that certainrefinement arcs are marked with a letter “R” for “restatement”,described below. Recall again that FIG. 25, FIG. 26, and FIG. 37 presentvarious stages of processing to present the DAG localized at node 1 as atree through which the user can explore nodes 12 and 15.

FIG. 40 shows the process of refining problem nodes 12 and 15 with a newproblem node (17) that addresses it with respect to node 1, usingiterated, in-place restatement of inherited nodes. FIG. 39, again, showsthe full resulting DAG after this process.

Similar variations to those described for standard iterating copying arealso relevant for iterating copying in-place.

This brings up the question of how to present the initial, localized DAGto the user in a way that avoids showing information that has beenrestated by the user as described above. Some embodiments might do thisimplicitly based on the DAG structure, such that at least thosestructures built with in-place restatements may be considered to berestatements in localization. They might require, for example, that if asolution directly solves some problem node and also refines othersolution nodes, that the refining solution be considered a restatementso that it is made visible in place of the refined nodes. This issimilar to a requirement that the refining and refined entities havedifferent objects. Other embodiments, including the one outlined furtherbelow, might create restatements explicitly, for example only when aninherited node is modified, so that the marked refinements could betreated differently upon localization. Such restatements would connectthe modified inherited node with the original, and any restating copiesof inherited node ancestors with the originals. Creation of restatementscan be constrained such that any entity restates at most one other (moregeneral) entity.

In either case, restatements can also form a basis for controllingaccess. Some embodiments may wish to prevent unrelated restatements,e.g., restatements that address a node not in the substructure orcontext, from being viewed. With implicit restatements, embodimentsmight, for example, avoid inheriting solutions that directly solve aproblem unless that problem is on the solution's inheritance path. Or anembodiment might, as described below under “Mutually ExclusiveRefinements” as “specializations of a problem by distinct geographicareas could safely be considered mutually exclusive”, support thedefinition of mutually exclusive refinements and avoid inheritingdescendants of a solution that address alternate refining problems. Wewill see below a method of controlling access during localization withexplicit restatements. The goals are both to avoid showing userssolutions that are not relevant to them and to ensure that solutions areonly visible to those who ought to see them (potentially funders of theorganization who share a wider goal, but not sibling organizations underthe same funder).

This way of using restatements is not only about controlling access butalso relevance. Consider an organizational hierarchy that is dependentupon a project hierarchy. Because the user is primarily concerned withthe project, they may likely not have interest in seeing subordinates ofindividuals assigned to the project if those subordinates are assignedas such with respect to work on an unrelated project (in this case, therelation of assignment of users to solutions may well be many-to-many).

Since for various embodiments an inherited restatement will appear inplace of the restated entity, it may be convenient for embodiments toplace other (non-restatement) descendants of the restated entity belowits restatement. Again, this may seem odd because of the local DAGdiverging from the global one, and some embodiments may choose to avoidtaking this step, particularly in the case of non-restatementrefinements. To be consistent with this approach, in FIG. 86 we modifyCollect Inheritance 2240 to inherit other refining nodes through arestatement.

The suggested method of in-place iteration triggers a restatement of theinherited nodes along the path from the node at which an operation isinitiated to the locus node. In the case of a “diamond” configuration,where, for example, the node at which an operation is initiated has twoparents, both sharing a common grandparent, the operation may beinitiated with respect to a single path through the diamond, causing oneparent to be restated but not the other. If a later operation isinitiated from the same node, or a descendant, that is accessed throughthe other parent, some embodiments may restate all inherited nodes onthe path the locus, while others may do so only any inherited prefix ofthat path. The former method may require noticing, upon working uptowards the locus, whether a node is constituent with its parent beinginherited, continuing all the way to the locus, and when working backdown, restating only inherited nodes but resetting parents of thoseconstituent nodes whose parents were restated.

We allow for restatements as a particular kind of refinement associationbetween entities of the same kind. The localization process on theserver may aggregate any restatements it encounters, as these may beneeded by the client in formulating appropriate server requests.

Primarily, we may wish to hide inherited entities that are restated by anode in the substructure. To make this easier, some embodiments use avariation of Record Inheritance 2250 that adds inherited nodes to theDAG bottom-up (i.e., inherited nodes closest to the substructure areadded first). For convenience, embodiments may use a shallowest-firstversion of Collect Inheritance 2240. In place of a single parent ortarget node that is to receive the inheritance, we maintain a stack oftarget nodes, and refer to the immediate recipient of the inheritance asthe top target node. An auxiliary routine now returns both whether ornot the subDAG was reached in the course of following inheriteddescendants, and the children placed under the top target node. Anotherroutine, Record Restating Child 2270 records each restating child of thecurrentEntity. Much of the work, including a check of proper ancestry,is intended to prevent the existence of redundant refinement links andcan be addressed as described above under “Explicit DAG Augmentation bySpecialization” as “prevent situations in which a direct refinementassociation is created where an indirect one already existed”. In ofthese routines, we branch based on whether or not child nodes arerestatements. Importantly, we perform this determination in a way thatignores some restatements, when some sequence of object-of operations onthe child yields the locus node or the child's object is on theinheritance path (instead, consider storing on each restatement thepreviously iterated augmentation upon which it is built and checkingwhether the sequence of these leads to the locus node—it corresponds tothe object in the case of an in-place restatement of a cross-kindaugmentation), treating them as non-restatements if in the subDAG orignoring them altogether otherwise. Furthermore, in order to userestatements for controlling access as suggested above in this sectionas “restatements can also form a basis for controlling access”, we makethe inheritance path available to Record Inheritance 2250. With thisrevision, that routine may skip over unrelated restatements. Here, weconsider a restatement of an inherited node to be unrelated if it has noparent on the inheritance path. This is shown in FIG. 87.

On the client side, some embodiments replace the alternative high-levelprocess flows presented in FIG. 80 and FIG. 81 with FIG. 89, which, ifappropriate, restates and then refines a single inherited node, althoughother embodiments may use variants of these other routines. FIG. 90,which we use in this case, differs from FIG. 83 primarily in that ituses atomic routines that perform restatement. It also maintains arecord of prior restatements. FIG. 91 displays a process flow thataugments the DAG while restating visualized nodes in-place for anexplicit refinement operation. We next present differences from FIG. 73.In identifying refinement paths from the object of each refined nodetowards the locus, we separate a chain of restatements of the objectfrom refinements of the original, restated entity. Then, in calculatingthe GLB, we work with the refinement paths. If the GLB is itselfinherited, recur on Restate Inheritance for Specialization 2133 torestate it and its ancestors. Then, replace GLB with its restatement onrefinement paths from refined entities and add the GLB restatement toeach corresponding restatement path. In generating the proof for DAGaugmentation, concatenate each restatement path from the restating nodeto the restated node with the corresponding refinement path from therestated node towards the locus. Otherwise, continue as with AtomicSpecializing DAG Augmentation 2141.

FIG. 92 presents the same routine with cross-kind as well asspecializing DAG augmentation.

Multiple Cross-kind Augmentation

Many-to-many cross-kind relations are not strictly necessary, in that ifthe refinement relation on the independent entity kind is many-to-many,it is possible to refine any number of independent entities collectivelyand associate the new dependent entity only with that refiningindependent entity.

In some cases, embodiments may wish to support many-to-many cross-kindrelations. Consider the DAG in FIG. 93 for an example of how it couldwork. Here we have a problem node with four children, two problems thatsolve it and two problems that refine it. FIG. 94 shows the same DAGwith navigation centered on the two child problems, prior toinheritance. After both child problems inherit both solutions, we havethe DAG in FIG. 95. From the exploration in FIG. 96 we perform arefinement of the two solutions, as shown in FIG. 97. As shown in FIG.98, in addition to the refinements, there is an implicit cross-kindassociation with each child problem. Clearly, by assumption here thereis no single problem assigned to each solution.

Embodiments that directly support many-to-many cross-kind relations mayconsider how to constrain the creation of a dependent entity associatedwith multiple independent entities and refining multiple other dependententities. One way is to require for each independent entity beingaugmented, and for each dependent entity being refined, an ancestorcross-kind association such that the independent entity is refined bythe independent entity being augmented and that the dependent entity isrefined by the dependent entity being refined. It is also possible,however, to partition the dependent entities among the independent ones(or equivalently, partition the independent entities among the dependentones) so that the ancestor cross-kind association need only exist foreach dependent and independent entity within the same partition.

The techniques above for making relative DAG augmentation intuitive andefficient can be adapted to creating dependent entities related tomultiple independent entities by the same cross-kind relation, as wellas refining multiple dependent entities, by having multiple locus nodes.Multiple locus nodes are useful for other purposes, including forgeneralization (described under “DAG Generalization”).

This can be accomplished using a slight generalization of our DAGs.Given a DAG Dag, for any entities E| we define the DAG Dag_(E)|¹ todiffer from Dag only in that Dag_(E)|¹ does not include any nodesneither reachable from some E in E| in Dag, nor any nodes from whichsome E in E| is not reachable in Dag.

A particular embodiment uses a further modification to the DAGs.Dag_(E)|² differs from Dag_(E)|¹ only in including as children of each Ein E| entities inherited by E, e.g., entities dependent upon an entityrefined by E.

This embodiment presents DAGs Dag_(E)|² with common context. Now, if theuser selects one or more nodes inherited by some E in E| (each of whichrefining a node directly inherited by E) from which to derive a refiningentity, a cross-kind association is implicitly formed between each E inthe context of an inherited node being refined and the new refiningentity.

Dag_(E)|¹ is obtained from Dag similarly to Dag_(E) ¹ as described aboveunder “Explicit DAG Augmentation by Specialization” as “Obtain Dag_(E) ¹from Dag by . . . ”, but beginning with multiple entities from which tosearch, including all structures encountered in a common reduced DAG andkeeping a common collection of visited nodes across E|.

Dag_(E)|² is obtained from Dag_(E)|¹ similarly to Dag_(E) ² as describedabove under “Leveraging Inheritance for DAG Exploration” as “obtainingDag_(E) ² from Dag_(E) ¹”, but calling Collect Inheritance 2240 for eachlocus node. Because the various locus nodes may share common context, itis beneficial to maintain a collection of nodes to be inherited for eachcontext node across any E in E|, using the precomputed inheritancesubsequent times an entity is encountered. Record Inheritance 2250 iscalled for each entity inherited by any locus node.

Where we had resorted to using “the locus node” in satisfying boundsacross both substructure and context, in embodiments where multiplelocus nodes are supported, it may be necessary to seek an underlyingbound of a tree (their shared substructure for a GLB or their sharedcontext for an LUB).

Many embodiments may ensure that locus nodes not be ancestors ordescendants of each other, at least not in the localized DAG, as thiswould complicate the notions of substructure and context.

In the case of a many-to-many relation and where no indirect objects arestored, with all loci being of the same kind, a user can jointly refinemultiple nodes that were inherited by separate loci, easily creating a“diamond” structure for each in addition to the final refinement.

Another potential benefit of all loci being of the same kind is that forgeneralization (as described below), a user can create a cross-kindassociation with the dependent entity refined by each of the loci.

Where there are multiple locus nodes, embodiments may omit auxiliaryinformation (described under “Auxiliary Information and Aggregations”)or may provide either or both of information relevant to “any” locusentity or “all” locus entities. Where the auxiliary information isdiscrete, this may just involve a union or intersection, respectively,over the auxiliary information of the various locus entities. Where theauxiliary information is hierarchical, as described below under“Secondary DAGs”, in the case where related entities are included in theauxiliary information via various locus entities, embodiments may aftertaking the union of the entities related to the various locus entities,remove those that are ancestors of entities auxiliary to another locusentity. Or for “all”, instead of intersection, consider nodes auxiliaryto a locus node only if, for each other locus node, they are related viarefinement to a node auxiliary to that locus node, and then include onlythe most general such auxiliary nodes. Thus, if one locus user isproficient in Java programming and product management, another in Pythonprogramming and product management, and a third in programming and agileproduct management, skills all selected users are proficient in wouldconsist of product management and programming, while skills any user isproficient in would consist of Java programming, Python programming, andagile product management.

Embodiments may often desire to have all loci be of the same kind, butthere are exceptions. To aid in matching users to project roles, thepool of users and pool of projects could all be made loci. Then,including the cross-kind relations directlyProficientInSkill anddirectlyRequiredBy, along with the direct refinement relations (at leastdirectlyRefinesSkill), it is easy to visualize how particular usersconnect to particular project roles via skills.

To deal with a need to match individuals to projects only if they meetall skill requirements, not just one, embodiments might treat bothdirectlyProficientInSkill and directlyRequiredBy as many-to-one ratherthan many-to-many and implicitly create a skill that refines each ofthose either required by the solution or in which the user isproficient. This would be helpful for embodiments where skillrequirements are tied to resource requirements (as described below under“Resources” as “skill requirements may be associated . . . with . . .human resource requirements”), but may not (as described below under“Recommendations” as “For embodiments where skill requirements are tiedto resource requirements . . . ”) be relevant for embodiments where theskill requirements are tied to the project as a whole.

Then for each multi-skill so created, the DAG could also include asparents of that skill each smaller combination of the same collection ofskills, up to the singleton skills which would also be included in theDAG. To avoid the clutter and inefficiency of so many DAG entries, itwould be preferable to include refinesSkill associations in place ofdirectlyRefinesSkill associations only as needed to connect existing DAGskill entities without redundancy. An index can be built from individualskill entities to the multi-entities from the DAG in which theyparticipate. Then, for each multi-entity, it is possible to look up theother multi-entities associated with each of its conjuncts, eliminatingitself and any multi-skills that contain single skills not components ofitself, and ordering the remaining ones by the subset relation overtheir sets of individual skills. Adjacent skill sets should be connectedin the DAG.

It may be possible to view a DAG with multiple loci in the case that itis a secondary DAG (as described below under “Secondary DAGs”) for whichmultiple entities are related to the loci of the primary DAG, or if theuser explicitly navigated to multiple nodes.

DAG Generalization

We have concentrated in the foregoing on top-down augmentation ofproject structure. But it is also useful to augment projects from thebottom up. A natural complement to specialization is generalization. Aparticularly useful case involves creating more general problems andsolutions from more specific ones. For entities of a kind that need notact as a dependent entity to any other entity, embodiments need notrestrict such upward refinement.

To justify maintaining the object assignment of the refining entities,some embodiments may enforce a correspondence constraint similar to thatabove under “Explicit DAG Augmentation by Specialization/Multiplesimultaneous refinement” for specialization. In assigning an independententity to a new dependent entity under a cross-kind relation where thedependent entity is refined by one or more existing dependent entities,embodiments may require that for each refining dependent entity, somerefinement descendant of the independent entity is related by the samecross-kind relation to (has as a direct object) a refinement ancestor ofthat dependent entity, indicating a form of correspondence (somewhatlooser than under the correspondence constraint above under “ExplicitDAG Augmentation by Specialization/Multiple simultaneous refinement”)between the new cross-kind association and some preexisting one. Thus,if a new refined (generalizing) dependent entity is created with anindependent entity as its object, the object of each refining dependententity must under various embodiments refine that independent entity.

For dependent entities of a kind that may be associated with zero or oneindependent entity (an example might be problems that may be componentsof zero or one solution), some embodiments might require that refiningentities should all have an object, or none should. In the former case,the new, generalizing entity may be assigned the LUB of those objects.In the latter case, the new, generalizing entity may not be assigned anyobject. Other embodiments might allow any generalization of dependententities of this kind to not have an object, and allow any number of therefining entities to have objects or not, but still require that if anobject is assigned to the new refined entity, that it be the LUB of anyobjects of refining entities.

For dependent entities that must be associated with an independententity, we can generalize several dependent nodes if we can calculatethe LUB of their objects as the object of the new, generalizing,dependent node. This may be possible especially but not exclusively ifthe nodes being generalized are in the substructure as are theirobjects. Otherwise, a cross-kind operation may be initiated from thenode of the independent entity with which the generalization is to beassociated, referred to as the base node. The association of a dependentnode with its object can be considered direct if there is a base nodeand it differs from the LUB, or otherwise it can be considered indirect.Embodiments, especially those that implicitly include the locus node inLUB calculations (as described below under “DAG Generalization/Multiplesimultaneous refinement” as “implicitly broaden the LUB inputs toinclude the locus node”), may require the base node to be in thecontext.

Thus, a user might want to generalize a dependent entity whilemaintaining or generating cross-kind relationships with independententities. The benefit is that after being generalized to apply to a moregeneral problem, that generalized solution may be inherited by otherspecialized nodes and refined to them as discussed previously. For abase (independent) node in the context (that a user may intend toaugment downward), instead of allowing a user to select dependent nodesthat the new dependent node should refine, an embodiment might allow auser to select dependent nodes of the same or at least consistent kind(some embodiments may restrict these to the context) that would refinethe new dependent node. The new node is then interposed between the nodebeing augmented and the refining nodes. This implies that the new nodemay be positioned above the refining node if this refining node is inthe context, or below the base node, if the base node is in thesubstructure. If the base node is in the proper context and the refiningnode is in the proper substructure, the new refined node would not bedisplayed by some embodiments, so embodiments may restrict refiningnodes to the context.

The user might select several entities of the same kind to jointlygeneralize. Consider the DAG in FIG. 99. Here, there are two chains ofproblem refinements of length 3, joining at the most general, 31, andeach terminating with a single solution (36 and 37). If the usernavigates to 31 and explores to 36 and 37, as in FIG. 100, theninitiates a joint generalization of 36 and 37, as in FIG. 101, the DAGin FIG. 102 is a possible result.

The user might instead explicitly select both an independent entity toextend with a cross-kind association and any number of dependententities to generalize. For example, a user might want to generalizesolutions with the intention of solving a particular, more general,problem. Consider the DAG in FIG. 103. It differs from FIG. 99 both inthat each dependent node directly addressing an independent node (46 and47) is already generalized by another dependent node (48 and 49,respectively) and in that the LUB 41 of the object nodes has arefinement parent 40. From the exploration in FIG. 104 we select forgeneralization the two dependent nodes (48 and 49) and initiate across-kind operation from root independent node 40 as shown in FIG. 105.As shown in FIG. 106, the new node 50 is now situated between theindependent node 40 it addresses and the dependent nodes 48 and 49 thatit generalizes.

In the above examples, the nodes to be generalized, selected explicitlyby the user, were refined by the locus nodes, whose objects refine thebase node. Where there is a more complex sequence of dependencies, aprocess analogous to that described for iterating specialization may berelevant to process the several generalization and cross-kindaugmentation operations in sequence, again progressing top-down. As withthat situation (described above under “Iterating DAG Augmentation” withregard to FIG. 213), it may be necessary to reveal nodes, this time inthe context. An analogous routine for accomplishing that is presented inFIG. 214.

It is possible when performing cross-kind augmentation of a base node inthe context, for embodiments to implicitly treat the path from the locus(or loci) up to but not including the base node as a sequence (orsequences) to be copied and generalized (via iteration) with theuppermost copied node being generalized by the new augmenting node. Asan example, consider FIG. 107. It has the structure of a problem withone refining problem that in turn has two child solutions, each of whichhaving a single component problem. We assume that we've navigated to thetwo component problems, 74 and 75 as locus nodes. If we initiate asolution from the root problem 70, this can be interpreted byembodiments such that that solution is refined by a copied portion ofthe context. In particular, we start with the loci, copying the twocomponent problems (as before, allowing the user to modify information)to generalizations, have those in turn componentize a new solution thatgeneralizes the two existing solutions and solves the root problem. Theresulting DAG is in FIG. 108.

Many aspects of generalization are analogous to specialization, but withthe substructure and context reversed (although we concentrate here ontop-down cross-kind augmentation in both cases).

FIG. 109 shows a hierarchical breakdown similar to that of FIG. 42.

Multiple Simultaneous Refinement

For embodiments that associate an independent entity with each dependententity of a particular kind, where several dependent entities are beinggeneralized it is reasonable to assign the least upper bound of theobjects of the nodes being generalized to the new entity. For example,we might desire that every solution be associated with a distinguishedproblem that refines any problem that it solves, or that every argumentsupport or oppose a distinguished object that refines any object that itaddresses. Unfortunately, as indicated above under “Explicit DAGAugmentation by Specialization/Multiple simultaneous refinement” as “orthe context as a subDAG for common ancestors”, the context tree providesquite limited access to least upper bounds. Incorporating inheritance(in the upward direction) may provide a possible solution in someparticular cases.

In calculating the LUB, analogously to the case of GLB described aboveunder “Explicit DAG Augmentation by Specialization/Multiple simultaneousrefinement” as “broaden the GLB inputs . . . ”, one has to considerwhether or not to implicitly broaden the LUB inputs to include the locusnode (assuming that it is refined by all of the objects, in thesubstructure, of nodes being refined). Doing so would again recognizethe significance of the user's having navigated to the locus as a signalof relevance.

We proceed to describe calculation of the independent node to relate tothe new refined dependent node as the LUB with respect to thesubstructure and context trees. If any dependent, refining nodes werenot selected from the substructure (they were selected from the propercontext), embodiments that enforce the correspondence constraint under“DAG Generalization” can safely assign the object of their GLB (in theinverted context tree, obtained using Calculate GLB wrt a Tree 0111), ifthat GLB exists, to the new refined node. Or in the case that all therefining dependent nodes (being generalized) were selected from thesubstructure, embodiments that enforce the correspondence constraintunder “DAG Generalization” can safely assign the object of their LUB(obtained using Calculate LUB wrt a Tree 0101), if that LUB exists, tothe new refined node. Some embodiments, though, may skip this step andsimply use the locus node, as described above in this section as“broaden the LUB inputs . . . ”. In the case that the dependent nodesbeing refined have the same object, we can assign that object to the newrefined node (again, this step may improve efficiency but can be omittedas it is covered by what follows). Otherwise (or for embodiments thatprefer to go directly to this approach), we may rely on the presence ofthe objects of the refining dependent nodes in the substructure orcontext trees and check for an LUB among them, using Calculate LUB wrtSubstructure and Context Trees 4101. Calculate LUB of Objects ofRefining Nodes wrt Substructure and Context Trees Explicit 5111 ispresented in FIG. 111.

Calculate LUB wrt Substructure and Context Trees 4101 assumes that itsinputs arrive in a node list and first confirms that all members are ineither the substructure or the context, failing otherwise. Where anynodes are in the context, the client calculates the GLB of those withrespect to the inverted context tree, using Calculate GLB wrt a Tree0111, and ignores those in the proper substructure. Where all nodes arein the substructure tree (and we haven't reverted to using the locus),it takes their LUB with respect to the substructure tree using CalculateLUB wrt a Tree 0101. Some embodiments might, in place of failingimmediately where indicated above, attempt to find the LUB in the DAGsby other means, such as a more exhaustive search.

In the example involving FIG. 99 through FIG. 102, presented above under“DAG Generalization”, 31 is assigned to 38 as the LUB of 34 and 35, theobjects of the nodes being refined. Note that in FIG. 101, the newsolution node 38 is created under problem node 31, as suggested aboveunder “DAG Generalization” as “or below the base node, if the base nodeis in the substructure”.

The server may now require validation that the object of each entitybeing generalized is itself generalized by the provided object of thenew node (for now the LUB of all such objects), i.e., that the object ofthe new node is at least an upper bound of the objects of the refiningnodes. The server may require for each dependent entity to begeneralized, a chain of entities related by refinement (we assume forconcreteness from most specific to least) from the object of thatdependent entity being generalized to the least upper bound. Such achain can be provided using the tree-based exposition of projectstructure. For each node being refined, the client can build the pathbased on one of several cases. For both the LUB and the refining objectin the context, the client reverses the result of tracing the pathtowards the root of the context tree from the LUB, following refinementsuntil a node is reached with the object of the entity at the refiningnode. For the LUB in the context and the object of the refining node inthe substructure, it can concatenate the path from the object node ofthe refining entity up to the locus with the reverse path from the LUBto the locus. Embodiments that do not implicitly include the locus nodein LUB calculations (by analogy to those described under “Explicit DAGAugmentation by Specialization/Multiple simultaneous refinement”) mayadd a case for the GLB (and the object node) in the substructure and inthat case use the path obtained by starting with the object node andascending though the substructure until reaching the LUB. An embodimentof the proof generation process is presented in FIG. 122, using GenerateProof Path 0113 from FIG. 59. In our example, if the user generalizesnodes 36 and 37, the proof for this embodiment will consist, for 36, ofthe path [32, 31] from its object, 34, to the LUB, 31; and similarly for37, of [33, 31] from its object, 35, to the LUB, 31.

On generalizing a node in the context, preferred embodiments will firstmove the node to the top of its parents node list (see below under“Presentation of Common Context of Multiple Inverted Trees”). If thenode from which the operation is initiated is then the uppermost node ofthe DAG, embodiments will place the entire DAG below (in the substrate)the new node, established within a new frame. Otherwise, the new nodecan be placed at the top of the node list of the enclosing frame.

Putting these pieces together, the client can use Atomic ExplicitGeneralizing DAG Augmentation 4141 to generate a single new node that isrefined by existing nodes. FIG. 110 describes the sequence forsituations where each dependent entity is assigned an object independententity as LUB with respect to the substructure and context of theobjects of the refining nodes. First, for each refining node, identifysequences of nodes related by refinement from its object through thesubstructure or context, towards the locus. Comments apply similar tothose presented above under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” as “Putting thesepieces together . . . ”. Then, calculate the LUB of the objects of therefining nodes as in FIG. 111. In the case that the LUB does not exist,fail and provide an error message. Use the LUB and its refinement pathin generating the proof for the server as in FIG. 122. Meanwhile, promptthe user for information to be stored with the new entity. Then accessthe server to request the augmentation operation, sending the proof. Ifit fails, clean up the partially-created node. Otherwise, update theclient information to include the new entity (creating a record for thenew entity including the user-entered data and its object, and updatingrecords for entities of the nodes being refined to include the newentity as an additional child). The server returns the databaseidentifier of the new entity, which can be used by the client, forexample to build a URL for the new node.

The proof validation process where every dependent entity is assigned anobject is as in FIG. 123. The server may confirm that for each refiningentity, the given path is in fact a chain of refinements, beginning withthe object of the refining entity and ending with the provided object ofthe new refined entity (generally the LUB of objects of the refiningentities). It follows the path provided through the global DAG,verifying that each step is a refinement.

With direct objects only, the proof validation process, Validate Prooffor Generalizing DAG Augmentation with Direct Objects Only 5231, is asin FIG. 53. The server may confirm for each refining entity, that thegiven independent path is in fact a chain of refinements, beginning witha purported direct object of the refining entity, and ending with theprovided object of the new refined entity (generally the LUB of objectsof the refining entities), that the given dependent path is in fact achain of refinements, beginning with the refining entity and ending withnew refined entity, and finally that the purported direct object of therefining entity is genuine.

Generalization of Inherited Nodes

Embodiments enforcing the correspondence constraint under “DAGGeneralization” can safely allow nodes inherited into the substructureto be generalized only if they are first copied as described above under“Iterating DAG Augmentation” and “In-place, Iterating DAG Augmentation”.This operation, however, then does not generalize the inherited nodeitself, but only a specialization of it. An inherited node can begeneralized directly only when creating a cross-kind association withthe node from which that node was inherited or one of its ancestors inthe context. Consider the example DAG from FIG. 24 where we assign anindependent node to each dependent node. If we were to navigate to node2 and initiate a cross-kind augmentation from that node while directlygeneralizing inherited node 10, then 10 and the new refined dependentnode would have objects of 1 and 2, respectively, but refinement runs inopposite directions, with 2 refining 1 but 10 refining the new node. Wecould perform the operation from nodes 1 or 0 in the context, but wecould just as well have navigated to either of those nodes first andthen initiated the operation with 10 not being an inherited node. Ifnode 10 is first copied to a refinement 10′, 10′ would have as object 2.When generalizing 10′ while augmenting 2, we would then be in thesituation described under “DAG Generalization/Single cross-kindaugmentation with multiple simultaneous refinement” and could proceedaccordingly.

If, however, an embodiment supports upward inheritance of certain kindsof entities into the context, such nodes could be generalized using thesame techniques presented previously for specializing inherited nodes inthe substructure.

Single Cross-Kind Augmentation with Multiple Simultaneous Refinement

To enable further reuse of solutions, users may generalize them, so thatthey address a more general problem. The general solution can then beinherited by other specialized problems (and then specialized to thoseproblems). More abstractly, to enable further reuse of dependententities, users may initiate a cross-kind augmentation from a selectedindependent node (the base node). The general dependent entity can thenbe inherited by (and specialized to) other specialized independententities.

Analogously to the case of GLB described above under “Explicit DAGAugmentation by Specialization/Single cross-kind augmentation withmultiple simultaneous refinement” as “guaranteed a path from the basenode to the object of each refined node”, refinement of the base node bythe LUB guarantees a path from the object of each refining node to thebase node and thus satisfaction of the correspondence constraint under“DAG Generalization”. Embodiments enforcing that constraint have similaroptions if such a path cannot be determined. To enforce the constraint,the LUB calculation can be performed as before, but the result comparedagainst the base node.

If the base node is the same as the LUB of the objects of the refiningnodes, it is redundant and embodiments may choose to consider suchaugmentations as simple refinements.

In cases where a cross-kind augmentation of an independent node isrequested along with generalization of a dependent node of which it isalready the object, it is still possible to insert a new node betweenthem, but when the independent node is made the direct object of the newdependent node, the independent node should be made merely an indirectobject of the existing dependent node.

Where every dependent entity is associated with an independent entityand the correspondence constraint under “DAG Generalization” isenforced, we can use the proof mechanism described above under “DAGGeneralization/Multiple simultaneous refinement”, with one modification.There is now a distinction between the base node and the LUB, so thatfor the independent paths various embodiments effectively concatenateeach path from the object of a refining node to the LUB with the pathfrom the LUB to the base node. Again, we pass the suffix path to theserver as part of the proof so that it need only be checked once. Theroutine, using Generate Proof Path 0113 to obtain the refinement pathfrom the LUB to the base (or failing if unsuccessful), is shown in FIG.126.

Concerns such as those stated above under “Explicit DAG Augmentation bySpecialization/Single cross-kind augmentation with multiple simultaneousrefinement”, including directlyAddresses being many-to-many, apply hereas well.

Again, another modification to the proof structure presented in FIG. 122is useful, in addition to that just described. The proofs now take theform of a suffix path from the LUB to the base node and, for eachrefining dependent entity, of two refinement paths: one to the refiningdependent entity and one to the LUB, each beginning with entities thatare in turn associated by the same cross-kind relation. The proofgeneration process is as in FIG. 127. For the example involving FIG. 103through FIG. 106, presented above under “DAG Generalization”, the prooffor some embodiments will be two pairs of paths, one for each node beingrefined (if indirect objects are available, only the independent(problem) paths need be provided). In each case here, following thesolution refinement hierarchy from the refining solution node towardsthe locus node and stopping at the object problem yields the existingproblem/solution pair corresponding to the new problem/solution pairbeing created by the current operation. For node 48, the dependent pathwill be empty for this embodiment because it is directly associated withindependent node 42 (with no refined solutions in between) and theindependent path will be [41, 40] for this embodiment because followingthese steps from the object 42 of 48 leads to the object 40 of new node50. Again, by convention we treat the initial nodes as implicit and donot include them in the paths.

The proof validation process with only direct objects is as in FIG. 129.The server may confirm that for each refining entity, the independentpath, leading to the provided object of the new refined entity startsfrom an object of the entity from which the dependent path, leading tothe refining entity, begins.

With indirect objects, proof generation in FIG. 126 and servervalidation in FIG. 128 need only operate on the indirect paths.

The steps for handling a single cross-kind and generalizing DAGaugmentation are similar to those of Atomic Explicit Generalizing DAGAugmentation 4141 in FIG. 110. They differ, analogously to thediscussion above under “Explicit DAG Augmentation bySpecialization/Single cross-kind augmentation with multiple simultaneousrefinement”, in the use of the routines above that are intended tosupport cross-kind and generalizing augmentation, including GenerateProof for Explicit Cross-kind and Generalizing DAG Augmentation withIndirect Objects 4122, Generate Proof for Explicit Cross-kind andGeneralizing DAG Augmentation with Direct Objects Only 4132, andGeneralizing Cross-kind DAG Augmentation 5202, as well as in adding astep to convert to the corresponding refinement operation (e.g., of thekind of the nodes being generalized) if the LUB (calculated with FIG.111 and FIG. 112) is the same as the base node. The routine is presentedin FIG. 125.

Generalization, Restatements, and Iteration

In the following discussion, we use problems and solutions, with across-kind relation of “solves” (and in the reverse direction,“componentize”), for the independent and dependent kinds, respectively,only for concreteness of presentation.

If restatements are to be used for controlling access as described aboveunder “In-place, Iterating DAG Augmentation” as “restatements can alsoform a basis for controlling access”, so that solutions can be sharedselectively among different organizations, we need to createrestatements not just when specializing a general solution but also whengeneralizing a specific one. In the case of specialization, thesolutions are restated for the more specific problem and then anyfurther refinement or componentization is private to the more specificproblem. When generalizing, the same two steps may apply, but we need togive the administrator of (or other user with responsibility over) themore general problem leeway to generalize it on the specific problem'sside of the restatement so that excessive information is not inheritedby other specific problems. One way to accomplish this is to perform thetwo steps separately. In the first, the administrator of the moregeneral problem would be able to “solve and generalize”: present themost general solution to their problem directly as a generalization ofthe specific solution, considered as a restatement (although thedifference may be more than substituting general terms for specificones), perhaps by navigating to a specific solution and initiating thisoperation from the general problem. In the second, an administratorwould be able to initiate “generalize to restatement” from the specificproblem: create a logical restatement of that most general solution tothe domain of the specific problem, but because the restating refinementwas technically already created, this operation serves to interspersethe new solution in place of the specific one as a restating of the mostgeneral solution, while creating a non-restating refinement of this newrestating solution by the specific solution.

The administrator of the more general problem might want to jointlygeneralize several separate solutions, perhaps constructed by differentorganizations in response to distinct specializations of the generalproblem. In this case, the administrator could navigate to thosesolutions collectively. The first “solve and generalize” step abovewould be performed once, yielding a most general solution and atechnical restatement association with each specific solution that mayadd considerable generality. Then, the second “generalize torestatement” step could be performed once for each specific solution.

Now, consider a situation where the administrator of the more generalproblem wants to generalize not just a high-level solution to theproblem, but solutions to component problems that were suggestedseparately for each specific problem. This may involve navigating to theseveral component solutions and initiating from the general problem asin the example involving FIG. 107 and FIG. 108, presented above under“DAG Generalization” without respect to restatements. Embodiments mayiterate through the various nodes on the paths from the general problemnode down to the locus nodes, first creating a most general high-levelsolution (and several restatement associations), then a most generalcomponent problem (and several more restatements), and finally (for thisexample) a most general component solution (and several morerestatements). Where there are multiple locus nodes, embodiments are notmerely iterating through a single path from the base node, but tracingthe tree from the base node to each locus node. While some embodimentsmay start with the base node and work towards the locus nodes, otherembodiments may start with each locus node and work towards the basenode, avoiding subpaths already traversed. With the representationdescribed below under “Presentation of Common Context of MultipleInverted Trees”, one approach involves iterating through each contextframe encountered for each parent node list among context descendants ofthe base node. Then the second step may be performed, initiated fromeach specialized component solution and generating another iterationthrough the path between it and the general problem.

Embodiments may trace the various paths from the context node from whichthe operation was initiated towards the locus nodes breadth-first, inthat entities in corresponding positions are generalized together, Thecorrespondence need not be exact but only approximate—as with iterationfor specialization (see above under “Iterating DAG Augmentation” as “notrefine every such inherited ancestor of the inherited node beingaugmented”), we can copy either the entire path or specific nodes, forexample corresponding to sections of paths connected by refinementassociations.

FIG. 113 through FIG. 119 present an example of generalizationfunctionality. We have a project here relating to disaster preparedness.FIG. 113 shows a project screen with a particular solution, “Let'sconstruct buildings on stilts!”, being selected. FIG. 114 shows requeststhat this solution, along with another, “Let's construct buildings frombricks !”, be opened together, as described under “Presentation ofCommon Context of Multiple Inverted Trees”. The result is in FIG. 115,where the common ancestor, “How can we establish reduced human sufferingfrom disasters?” is visible and the operation “Propose a generalizingsolution” selected. The embodiment proceeds in FIG. 116 to allow theuser to edit the name of the new solution, “Let's mitigate the effectsof disasters!”, which solves “How can we establish reduced humansuffering from disasters?” and generalizes both “Let's mitigate theeffects of wildfires!” and “Let's mitigate the effects of floods!”,which are the next non-refining children on the path from the commonancestor to the locus nodes. The new node happens to be placed as aparent of “Let's mitigate the effects of wildfires!”, above its existingparent. The embodiment continues generalizing nodes along the paths tothe loci in FIG. 117. Since the following nodes (the loci) refine theirparents along this path, the new node, “Let's ensure adequateinfrastructure is in place to withstand disasters!” refines the nodejust created, while generalizing the loci themselves, as is evident fromthe result in FIG. 118. For embodiments that use restatements ingeneralization as described below, upon navigating to “How can weestablish reduced human suffering from wildfires?”, we cannot see thesuggestion regarding stilts, which would not be appropriate or helpful.Upon navigating to “How can we establish reduced human suffering fromearthquakes?”, as in FIG. 119 we can see the generalized solutions,which might next be refined, for example to “Let's ensure that buildingsare bolted to slab!”.

The administrator of the specialized project (we use the “floods”project here) might also wish to take advantage of the additionalgeneralization, and can do so by selecting “Generalize to restatement”on “Let's construct buildings on stilts”, as in FIG. 120, and typing thegeneralization, as in FIG. 121. Other embodiments may formulate thisdifferently, for example by initiating the operation from the node ofthe new, generalized entity.

For specialization, we allowed the user to select nodes to be refined inaddition to any node being augmented by a cross-kind relation. It wasclear whether each such node was inherited or not, and the inheritedones clearly needed to be specialized, along with their path to thelocus node. Here, embodiments may or may not allow the user to selectnodes to be abstracted in addition to any nodes on the paths from thenode being augmented by a cross-kind relation to locus nodes. Ifadditional nodes are permitted to be selected for abstraction, theabstraction may be assumed to relate to the nodes themselves or toabstracted copies of paths from the locus nodes, or the user may bepermitted to specify which treatment is desirable.

FIG. 130 shows a hierarchical breakdown for iterating generalizationsimilar to that of FIG. 62 for specialization.

A process for iterating abstraction with a cross-kind augmentation is asfollows. We copy one node for each contiguous path of the same entitykind, as suggested above under “Generalization, Restatements, andIteration” as “for example corresponding to sections of paths connectedby refinement associations”. A list is maintained of the locus nodes notyet reached. First scan descendants of the base node until any of thefollowing are reached: an occurrence of the same cross-kind relationbeing applied—the embodiment collects the dependent nodes reached inthis way; a different cross-kind relation than that being applied—theembodiment fails; a locus node—drop this node from the list of locusnodes not yet reached. Create a new cross-kind association with a newdependent node that is set as being refined (using a restatingrefinement if supported by the embodiment) by each collected dependentnode. If there are any dependent nodes, now consider them to beindependent nodes and for each repeat the above process, except that thecross-kind relation is initially left indeterminate and is set whenfirst encountered in scanning descendants. This process is described inFIG. 131. Note that although restating abstractions may be generated bythis process, some embodiments may not perform the updates in-place.

If there were multiple sets of related component solutions, the aboveprocess could be performed once for each, but generalization of thehigh-level solution would only be performed during the first pass; laterthe restatement would be identified.

In embodiments without explicit restatements, the basic methodologydescribed above of navigating to the specific and then initiating across-kind augmentation from the general, iterating though the paths,can still be applied.

Combining Specialization and Generalization

While some embodiments may treat specialization and generalization asentirely independent of each other, others may accept refined andrefining nodes together: the client, either by a distinct selectionoperation or merely checking each direction; the server, either byaccepting a direction with each dependent node, or merely checking eachdirection (e.g., in validation if the first step fails, try the otherdirection).

Combining specialization and generalization allows for interposing anode between two existing nodes in a refinement relation. This is usefulfor the “generalize to restatement” operation described above under“Generalization, Restatements, and Iteration”.

Combining specialization and generalization is also useful for extendingthe notion of iteration over inherited nodes described above to caseswhere a constituent (non-inherited) base node is modified or augmentedand one or more inherited nodes occur on the path through thesubstructure to the locus node. Embodiments may then wish to copy orrestate those inherited nodes prior to operating on the base node. Theentity at the new node created for an inherited node immediately above aconstituent node on such a path would need to be placed below theinherited entity and above the entity at the following constituent node.In these cases, however, the base node would always also be reachablefrom the same locus node by a path including only constituent nodes, sonot all embodiments will deem this step to be necessary.

In this case, the object of the new node may not be the LUB of theobjects of the refining nodes, but only be refined by their LUB and maynot be the GLB of the objects of the refined nodes, but only refinetheir GLB. Indeed, the base node under our constraints will refine theobject of each refined node and be refined by the object of eachrefining node.

DAG Refinement of Existing Entities

Embodiments may support establishment of a refinement relationship onexisting entities. One motivation here is to allow the process ofcross-kind augmentation with simultaneous refinement to be broken apart,so that the cross-kind augmentation happens first and one or morerefinement associations added later. Another is to support socialinnovation, whereby refinement associations are created between existingprojects.

For a kind of entity that does not participate as a dependent kind in across-kind relation, embodiments can establish a direct refinementassociation between entities at arbitrary nodes. To minimize thecreation of redundant associations as discussed above under “ExplicitDAG Augmentation by Specialization” as “prevent situations in which adirect refinement association is created where an indirect one alreadyexisted”, embodiments may allow such direct refinement associationsbetween entities at nodes either both in the substructure or both in thecontext and not connected by a path to the locus.

If independent entities are optionally assigned to dependent entitiesand the refining dependent entity has no such object (even indirectly),after the refinement association is created the object of the refineddependent entity (if any) may become the indirect object of the refiningdependent entity without any validation requirement.

If independent entities are assigned to dependent entities and thecorrespondence constraints under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” or “DAG Generalization”are enforced, if the refining dependent entity has an object (evenindirectly) we require that the refined dependent entity also have anobject and that a refinement relationship exist between the objects ofthe nodes being connected, generally in the same direction. As a specialcase, if the refining dependent entity and the refined dependent entityhave the same object, the refining dependent entity directly, therefining dependent entity's object is made indirect. The server mayrequire proof of such a relationship; if indirect objects are available,this can take the form of a sequence of nodes connecting their objectsthrough direct refinement associations, otherwise refinement chains fromthe dependent nodes to ancestors to which their objects are directlyconnected may also be required. Validation of the proof on the serverside is not much different than for other cases.

In the case of adding a refinement association with respect to across-kind association (e.g., where both dependent entities have objectsunder the same cross-kind relationship), this can easily be specifiedusing hierarchies by making the independent entity of the refinedassociation (the object of the refined dependent node), or one of itsancestors, the locus, and selecting both the refined and the refiningdependent entities in the substructure (they can often be distinguishedexplicitly or by the positions of their objects, as, for example, theobject of the refined dependent node being on the path from the objectof the refining dependent node to the locus). A proof can be generatedas the path from the object of the refining dependent node towards thelocus, until reaching the object of the refined dependent node. Thisformulation is most appropriate or convenient for creating refinementassociations where the refining dependent entity has an object, eitherbetween entities within an organization's projects or if twoorganizations are involved, where initiated from the organization of therefined project, since one of its projects must for various embodimentsbe the locus. An advantage of this formulation is that it is possible tocreate a refinement association between inherited nodes by performing aniterated copy (in-place or otherwise), as described above under“Iterating DAG Augmentation” and “In-place, Iterating DAG Augmentation”.

If independent entities are not assigned to dependent entities, thenembodiments can, as before with regard to augmentation, infer the objectof a dependent refined node in the substructure to be the firstindependent node immediately following a refinement chain of dependentnodes on a path to the locus. Embodiments can also require that therefining node be selected from a position immediately under its object(connected via a cross-kind association corresponding to the initialpart of a specialization operation as discussed above). The refinementpath can be obtained as the path from this object of the refining nodethrough the substructure towards the locus until reaching the object ofthe refined node.

An example of adding specialization to a cross-kind association is shownbefore the operation with navigation at node 61 in FIG. 132. Each set ofjagged lines represents an arbitrary refinement path. The user hasexplored through the substructure to refining dependent node 66, passingthrough its object, 62, and to refined dependent node 64. The DAG afterthe operation is as in FIG. 133.

This process Client DAG Augmentation with Refinement between ExistingNodes (in Substructure) 0106 for creation of a refinement associationbetween existing entities in the substructure via this formulation isdisplayed in FIG. 134 and FIG. 136. Begin by checking that both nodesbeing refined are in the substructure (although this may not be strictlynecessary in all cases). If necessary, distinguished the refined nodefrom the refining one. As previously with iteration, use CopyInheritance for Specialization 2103 or Restate Inheritance forSpecialization 2133 to obtain new constituent nodes in place ofinherited ones. Next, generate the proof as the refinement path from theobject of the refining node (as copied) to the object of the refinednode (as copied), using Generate Proof Path 0113 from FIG. 59. Thenproceed with creating the association, with Atomic DAG Augmentation withRefinement between Existing Nodes 0126. The operation is requested fromthe server, and if successful the new association may be recorded in theparent and child links of the local DAG. The object of the refining nodemay also need to be adjusted, as described above in this section as “maybecome the indirect object of the refining dependent entity” (this wouldneed to occur on the server as well). Finally, embodiments may make theresult of this operation evident by moving the subtree under therefining node under the refined node.

Alternatively, another formulation can be used for adding a refinementassociation with respect to a cross-kind augmentation. The user cannavigate to the refined and refining dependent entities as dual loci,and explore through their respective contexts to find a common ancestor(as under “Presentation of Common Context of Multiple Inverted Trees”),the object of the refined dependent entity and a refinement ancestor ofthe object, under the same cross-kind relationship, of the refiningdependent entity. To aid in proof generation, the path from the refiningdependent entity should go through its object. This formulation is mostappropriate or convenient for creating refinement associations where therefining dependent entity has no object (so can't be located byexploration) or if two organizations are involved, where initiated fromthe organization of the refining project, given an incremental way tonavigate to the two nodes from alternate projects that are beingassociated.

We next revise the example to demonstrate this alternative formulationfor the same initial DAG from FIG. 132 (this time with navigation atrefined dependent node 64 and refining dependent node 66). The user hasexplored through the object (62) of 66 to the common ancestor (61), alsothe object of 64. The resulting DAG after the operation is still as inFIG. 133.

This process Client DAG Augmentation with Refinement between ExistingNodes (as Loci) 0116 for creation of a refinement association betweenexisting entities as loci via this formulation is displayed in FIG. 135and FIG. 136. Again, if necessary, distinguish the refined node from therefining one, this time as loci. Attempt to reveal the object of therefinedLocus in the context as a common ancestor of refinedLocus andrefiningLocus, if not already so revealed, and then confirm that theobject of refiningLocus is on its path to the object of refinedLocus.Generate the proof as the refinement path from the object of therefining node (as copied) to the object of the refined node (as copied),using Generate Proof Path 0113. Then proceed with creating theassociation, with Atomic DAG Augmentation with Refinement betweenExisting Nodes 0126 (as described above under “DAG Refinement ofExisting Entities” as “Then proceed with creating the association”).

By this approach, the simultaneous cross-kind augmentation andspecialization or generalization presented above can often be directedas a two-part process: first creating the cross-kind augmentation andthen adding the relevant refinements. At that point, embodiments may ormay not choose to preclude augmentation operations from includingspecialization, either at the level of the client or server or both.

Preventing Cycles

With either creating links between entities at arbitrary nodes, ormoving a subtree from one node to another (moving, as described under“Cutting and pasting”, requiring detachment of one link and creation ofanother), there is a potential for creation of a cycle. Embodiments willlikely not want users to be in the position of scrolling endlesslythrough the same entities while exploring substructure or context, andmay take various steps to prevent it.

In the case where a link is created from a child in the substructure toa parent on the path from the child to a locus or in the context, orsimilarly to a parent in the context from a child on the path from thelocus to the parent or in the substructure, there is no danger ofcreating a cycle. Also, if both nodes have objects, the constraint checkmay preclude creation of a cycle. These guarantees, however, may not besufficient for many purposes.

One approach for preventing cycles when linking entities at arbitrarynodes is to perform, upon a request to create a link from one node toanother, a search of the ancestors of the node that is to be the parentor the descendants of the node that is to be the child, looking to findthe other node. If it is encountered, establishing the link would createa cycle, so the linking operation should not proceed without rectifyingthe problem.

If the entities to be linked are at locus nodes, their substructure andcontext has already been passed to the client, at least in part (seeunder “Explicit DAG Augmentation by Specialization” as “embodiments mayplace limits”), so that a search may be initiated. If the DAG is notvery large, it is quite reasonable to perform this search, triggeringdeferred accesses where necessary, but otherwise it can be inefficient.If the entities are not at locus nodes, the server would need to performthe search for cycles.

It is possible for embodiments to not perform any check and thus allowcycles to be created. In that case, cycles may be detected after thefact. It may be undesirable to create a cycle in the local(non-deferred) DAG, so embodiments may want to prevent these. Thatinvolves both checking for actual cycles in the initial DAG and uponunfolding deferred nodes, and also checking for potential cycles priorto allowing any linking operation. Embodiments may arrange for thesechecks to be performed on the client or on the server.

One option for dealing with the checks in the initial DAG and uponunfolding deferred nodes is to have clients check for cycles during theunfolding process. The client can detect cycles by checking, whenunfolding the context with respect to a locus, for elements of thesubstructure (including the locus) or of the path in the context fromthe locus to the node being unfolded, or vice versa. This may only benecessary the first time a node is unfolded during a session. If theuser requests a connection between locus nodes, the client could checkfor potential cycles as just described but without expanding anydeferred nodes. If the client identifies any cycle, it should inform theserver of the problem, passing it the offending path. The server canthen validate that the path is indeed a cycle in the global DAG. Someembodiments might have the server break the cycle, while others mightdisallow the operation. The server might select a link to break, perhapsthe one created by the least trusted user. It might also notify theadministrators of the various projects, so that they can provide theirconsensus of where the problem lies.

It is also possible for the server to perform similar initializationchecks prior to sending the localized DAG to the client, or prior tosending the result of expanding a deferred node.

If multiple clients request the same locus nodes at the same initialdepth with no intervening linking, it is not necessary for the samecheck for cycles to be done multiple times. In these cases, the servercould keep a “safe depth” for every entity to indicate whether cyclesare possible within that depth. The structure could be augmented eachtime a new entity is requested (or created) and the depth incrementedafter the node has been proven safe at that greater depth. If arequested node/depth is guaranteed safe, no cycle check is needed. Ifnodes within depth range are linked, the server may reset the safe depthfor all locus records within the old safe depth of both nodes.

Additional Project Structure

Additional Problem Structure: Data Measures

It is discussed under “General Data Sets” how data sets are specifiedwith the source of the database, conditions that must hold for dataitems to be selected, and expressions of the attribute values extractedfrom those data items, and how they may be associated with projects andaggregated based on user exploration of a localized DAG. Alternatively,data sets can be aligned much more closely with a particular problem,such that the problem consists entirely of increasing or decreasing aparticular attribute value. We refer to the specification of such a dataset as a data measure. With data measures, as above, each node isassociated with a query that may return particular attribute values ofparticular data items. The item set of a refining data measure, however,will for various embodiments be a subset of that of a refined datameasure. Thus, if one data measure refines another, it will for theseembodiments include attribute values associated with fewer selecteditems. For example, particular data measure problems might relate toraising the income of particular demographic groups such as elderly,minorities, or refining both, income of elderly members of a minoritygroup. A refining data measure might also extract additional attributevalues. The data problem may need to specify whether the probleminvolves increasing or decreasing that attribute. Upward anddownward-pointing arrows, respectively, can be incorporated into iconsfor these data measure problems.

As an example of the allowable structure of conditions, they might beconjunctions or disjunctions over constraints on individual attributevalues, or any nesting of these. Terms may reference the database,table, and attribute. The structure of conditions may vary amongembodiments. A simple grammar is as follows:

-   -   Condition|=ε|Term|∧(ConditionList)|∨(ConditionList)|ø    -   ConditionList|=<Condition,>⁺ Condition    -   Term|=Attrib|=Expr|Attrib≠Expr|Attrib>Expr|Attrib<Expr|ø    -   Expr|=Attrib|Const    -   Attrib|=(DatabaseName, TableName, AttribName)        Lists of both disjuncts and conjuncts are unordered, but a        standard ordering may be imposed. The null symbol allowable as a        Condition or a Term will be explained shortly.

Some such embodiments may imbue additional constraints to reduce thenumber of representations of any imposed ordering. A grammar thatrequires conjunctions and disjunctions to have at least two elements andrequires their alternation is as follows:

-   -   Condition|=ε|Term|(Conjunction)|(Disjunction)    -   Conjunction|=<DisjunctionOrLeaf∧>⁺ DisjunctionOrLeaf|ø    -   ConjunctionOrLeaf|=(Conjunction)|Term    -   Disjunction|=<ConjunctionOrLeaf∨>⁺ ConjunctionOrLeaf    -   DisjunctionOrLeaf|=(Disjunction)|Term        The definition of Term is unchanged from that above.

Embodiments that wish to maintain such a convention but allow users toperform operations that violate it can apply rules as follows to restorethe convention:

-   -   ∧(Condition)⇒Condition    -   ∨(Condition)⇒Condition    -   ∧( . . . , ∧(ConjunctionArgs), . . . )⇒∧( . . . ,        ConjunctionArgs, . . . )    -   ∨( . . . , ∨(DisjunctionArgs), . . . )⇒∨( . . . ,        DisjunctionArgs, . . . )    -   ∧( . . . , ε, . . . )⇒∧( . . . , . . . )    -   ∨( . . . , ε, . . . )⇒∨( . . . , . . . )    -   ∧( . . . , Term₁, . . . , Term₂, . . . )⇒∧( . . . , Term₂, . . .        , . . . )    -   ∧( . . . , Term₂, . . . , Term₁, . . . )⇒∧( . . . , Term₂, . . .        , . . . )    -   ∨( . . . , Term₁, . . . , Term₂, . . . )⇒∨( . . . , Term₁, . . .        )    -   ∨( . . . , Term₂, . . . Term₁, . . . )⇒∨( . . . , Term₁, . . . ,        . . . )        where in the last two rules, Term₂ refines Term₁. These rules        remove singleton collections, nonalternating nested collections,        embedded empty conditions, and redundant terms. Additional rules        might sort the ConditionLists using the standard ordering as        described above. For convenience, we switch here to the prefix        notation used for plans. Embodiments that modify this or the        above grammar to more naturally consider negations as general        conditions would need to, within an odd number of negation        forms, treat conjunctions as disjunctions and vice versa for        purposes of rules by which refining conditions may be generated.

Going further in this direction, conditions might be maintained indisjunctive normal form (DNF), conjunctive normal form (CNF), or anyother convention. It is possible to allow conditions to be entered andmaintained in the form of the simple grammar above, but checking whetherone condition refines another may require converting them to a normalform. A DNF grammar is as follows:

-   -   Condition|=(<Conjunction ∨>*Conjunction)    -   Conjunction|=(<Term ∨>*Term)|ø

A data measure problem may only be specialized by another data measureproblem with the same polarity (or with at least those possiblyextended, and possibly more data measures). Refining data measureproblems will for various embodiments have conditions required to holdover selected items at least as restrictive as those of the refined datameasure problems.

There is some similarity between conditions and the situation with plansdescribed under “Additional Solution Structure: Plans”, and many of thesame design options are relevant. Unlike conditions, plans do not have apolarity nor any notion of negation.

Data measures may be a special kind of problem that refines more generalproblems, or any problem may have the potential to add a data measure.

When refining multiple solutions, embodiments may well check forconsistency of their conditions. When augmenting the DAG with a newproblem node that specializes or generalizes existing problem nodes, anembodiment should ideally provide the GLB or LUB respectively of theconditions of augmented problem nodes, allowing the user to edit them tobe more or less strict, respectively. These can be calculated by forminga term for the GLB as X∧X′ or the LUB as X∨X′ and applyingsimplification rules to restore the appropriate form. Alternatively, adirect calculation could be derived depending on the condition formenforced by the embodiment. Embodiments, for example, could specializeconditions as follows to maintain alternation, as defined by the grammarabove in this section as “A grammar that . . . requires theiralternation”. If more than one condition is a conjunction or term(singleton conjunction), form a conjunction of the union of their terms,dropping any that generalize terms from another conjunction. Then,include each disjunction as an additional conjunct, dropping any thatare equal to or strictly more general than others, having additional ormore general disjuncts or lacking certain conjuncts or having othersmore specific. To maintain DNF as defined by the grammar above in thissection as “A DNF grammar is as follows”, with or without first takingthe prior step, embodiments can treat each condition as a disjunction ofconjunctions, and form tuples of their conjuncts (treating terms assingleton conjunctions). Sort in order of increasing length and removeany that include all conjuncts of (or generalizations of conjuncts of)an earlier tuple. The condition may be formed as a disjunction ofconjunctions, each tuple providing a set of conjuncts. The process forgeneralizing conditions is similar, reversing conjunctions anddisjunctions, as well as generalizations and specializations.

One possibility is to store the full condition with each data measureproblem. This avoids some of the complexity of dynamically formingconditions. An obvious disadvantage is the amount of space required.There is also an issue, however, of maintaining the required refinementrelation across conditions (derived from the refinement hierarchy ofdata measure problems) as those conditions are modified. The relation onconditions can be maintained naively by simply insisting that it not beviolated. If a condition were edited to be more specific (perhaps usingthe operations below), the result would need to be checked against itsrefinement children to ensure that it is still more general than each ofthem. If it were edited to be more general, the result would need to bechecked against its refinement parents to ensure that it is still morespecific than each of them. Thus, if a condition (or portion of acondition) is fixed over a series of refinements to the data measureproblem and later needs to be changed in each position, it may benecessary for the user to modify each of these separately, from the mostspecific to the most general, if specializing, or from the most generalto the most specific, if generalizing. It is perhaps more practical toautomate the process. Embodiments taking this approach might, uponspecialization of a condition, propagate that specialization throughrefinement descendants of the data measure problem, until reachingleaves or data measure problems whose condition is already at least asspecific. Similarly, upon generalization of a condition, they mightpropagate that generalization through refinement ancestors of the datameasure problem, until reaching leaves or data measure problems whosecondition is at least as general. In applying a change made to one termX to another, modified term X′, embodiments may replace the descendantterm X′, in the case of specialization, with the GLB of X and X′ or inthe case of generalization, with their LUB as described above in thissection as “These can be calculated by . . . ”. This would also allow arefinement association to be created between existing data measureproblems, where the condition of the refining problem does not refinethe condition of the refined problem, by propagating in eitherdirection. Either of these approaches would likely require changes tothe conditions to be permitted only for locus nodes, so that thesubstructure and context DAGs are available, or else require that theoperation be performed only on the server, with the client notified ofany violations of the refinement relation, or of all necessary changesto conditions.

An alternative is to treat condition components as entities, related toeach other and to data measure problems, and subject to inheritance.Entities may thus include conjunctions and each kind of term(disjunctions may be implicit if disjunctive normal form is maintained).Various kinds of relations might be supported on condition components:component relations, indicating the grammatical structure as suggestedabove; a refinement relation, corresponding tospecialization/generalization of the condition components; a movementrelation, indicating that a subtree is repositioned under a target nodein the refined condition, and an operand relation, a generalization ofthe component relation indicating that particular condition componentscan be manipulated in some way to yield some not clearly identifiedcondition component. The condition at a particular data measure problemcould be constructed by following its component descendants. Allcondition refinement associations should be considered to berestatements (as described under in-place iteration), in that inheritedrefined conditions need not be displayed if the refining condition isdisplayed and in that the refining condition need not be displayed if itis for an unrelated problem. Some embodiments may integrate conditioninformation with the local DAG of which the problem is the locus. Inthis case, it may be natural to display restating condition components,movement associations, and operator applications that relate to anancestor or descendant of the locus problem node. Some embodiments mayseparate the local problem DAG from the local condition DAG, with thelatter containing only the components of the condition for the locus ofthe local problem DAG. Such embodiments may still maintain an integratedlocal DAG or modified version thereof for purposes of enabling dynamicexploration of data as described below in this section as “may arrangeto label the refinement associations between problems . . . ”.

As an implicit GLB is performed upon the conditions of problems that arecollectively refined, specializing operations may be signaled by markersplaced in the structure of conditions. Operations for specializationmight be as follows:

-   Merge Disjuncts (conjunctions) This operation, relating to Merge    Orderings for plans, can take the form of a user refining inherited    conjunctions (initiating the operation from a base node and    selecting others) in the same disjunction. In DNF, disjuncts are    always conjunctions, but this can be the case in a more general    setting as well. In the localized DAG, the conjuncts of the selected    conjunctions are moved to the base node conjunction, removing    duplicates, and the selected conjunctions removed. In the global    DAG, a new conjunction restates each of those inherited ones, so    that it can inherit their descendants.-   Remove Disjunct This operation has no correlate for plans. This can    take the form of a user deleting an inherited disjunct. In DNF, such    disjuncts may always be conjunctions but in a more general setting    they can be any condition expression. In the global DAG, that    disjunct is restated by a null term, which need not be displayed to    any user, with respect to the locus problem.-   Add Conjunct (term) This operation relates to Add Unordered Leaf for    plans. In DNF, this can take the form of a user augmenting an    inherited conjunction with a new term. Embodiments simply place the    new term as a construction under its parent in the localized DAG,    but arrange that in the global DAG, the term be placed as a    construction under a new conjunction that restates the original with    respect to the locus problem. This new conjunction may operate over    the new term in addition to inheriting the operands of its parent.    In a more general setting, related operations can be used to    generate an initial term in an empty condition (which need not    create a conjunction) or to replace a term with a conjunction of    itself and a new term.-   Specialize Terms This operation relates to restatement of motivated    problems for plans. One term refines another if it is consistent    with that second term and contains at least as much information.    Refinement of terms might be defined as follows:    -   a>m refines a>n if m>=n    -   a<m refines a<n if m<=n    -   a=m refines a>n if m>n    -   a=m refines a<n if m<n    -   a>m refines a≠n if m>=n    -   a<m refines a≠n if m<=n    -   This operation can take the form of a user refining inherited        terms, the operation being initiated from any one of them while        selecting any others from the same conjunction. The user would        edit the inherited base node term, replacing it and the selected        term in the local DAG with a refining term, but creating a        restating refinement of each of those terms in the global DAG.        Refinement with each of the parent terms may be verified by the        server and possibly the client as well. If the client performs        the verification, it can indicate to the server which        term-refinement rules were applied.-   Conjoin Disjuncts This operation, related to Impose Order for plans,    inserts a conjunction within a disjunction. It may not apply to DNF    (without first reformulating), except in a trivial case that can be    handled under Add Conjunct. A user might initiate this operation    after selecting the disjuncts to conjoin. In the local DAG, these    may be moved to be children of a new conjunction that is created as    a child of the disjunction. In the global DAG, the conjunction may    be created as a construction under a new disjunction that restates    the original with respect to the locus problem (as with Add    Conjunct), and then “movement” arcs created from the new conjunction    up to the operand disjuncts, to indicate that they are considered to    move back down to the conjunction. This may be more straightforward    for embodiments that store the locus problem with respect to which    the operation is performed on the movement arc, as suggested    parenthetically for restatement refinements above under “In-place,    Iterating DAG Augmentation” as “storing on each restatement the    previously iterated augmentation upon which it is built”.-   Embed Conjunction This operation, related to Embed Order for plans,    pushes a conjunction disjunct into a disjunction descendant of a    sibling disjunct. It does not apply to DNF (without first    reformulating) but does apply in more general settings. The user    initiates the operation, specifying the object conjunction and    target disjunction, both available in the substructure as    descendants of the conjunction's parent disjunction. In the local    DAG, the object is moved to become a child of the target. In the    global DAG, some embodiments may create a movement arc between them,    pointing to the locus problem.-   Extract Disjunction A disjunction conjunct of a conjunction that has    a conjunction proper ancestor may be moved to be a child of that    conjunction ancestor. If there is no such ancestor, it may be    created as the root of the condition.

The latter two operations introduce “movement” arcs. Record Inheritance2250 may be modified from that in FIG. 87 so that movement arcs may betreated similar to restatements except that where embodiments replacethe restated node with the restatement, the object node of a movementarc is detached from its context and placed under the target node.

Corresponding generalization operations would be:

-   Split Disjunct (conjunction) The user might require that not all    conjuncts must be true together, but rather that various    combinations of them must hold together. This can be formulated as    allowing the user to partition the set of conjuncts in the condition    to be generalized.-   Add Disjunct (conjunction) This could be initiated from the    disjunct. The user might specify each conjunct.-   Remove Conjunct This could be initiated from the conjunct to be    removed. In DNF, the conjunct would always be a term.-   Generalize Conjuncts (terms) This could be initiated from any term,    while selecting any other terms from the same conjunction.-   Disjoin A conjunction node immediately under a disjunction can be    removed. This differs from Remove Conjunct in that the conjuncts are    not removed, but made into disjuncts of the conjunction's parent    disjunction.-   Extract Conjunction A conjunction disjunct of a disjunction with a    disjunction proper ancestor may be moved to be a child of that    disjunction ancestor.-   Embed Disjunction This operation pushes a disjunction conjunct into    a conjunction descendant of a sibling conjunct. It does not apply to    DNF (without first reformulating) but does apply in more general    settings. The user initiates the operation, specifying the object    disjunction and target conjunction, both available in the    substructure as descendants of the disjunction's parent conjunction.    The path from the target to the parent conjunction can be passed to    the server to help it validate the operation. In the local DAG, the    object is moved to become a child of the target. In the global DAG,    some embodiments may create a movement arc between them, pointing to    the locus problem.

Embodiments may need to adjust the operations depending on the form ofrepresentation of conditions. All operations, however, must serve tomake the condition more specific. They must, therefore, preserve anyfalsity of the refined conditions when specializing (or truth of therefining conditions when generalizing).

Operations may overlap in their scope to some extent or be restricted toavoid such overlap. For example, embodiments supporting Merge Disjunctsmay assume that at least one of the disjuncts being conjoined are termssince, if all were conjunctions, applying Conjoin Disjuncts andsimplifying would yield the same result as under that operator, and ifany were disjunctions or negations, one could simplify prior to applyingthe operator. Likewise, embodiments supporting Conjoin Disjuncts onconjunctions and simplifying the result need not support MergeDisjuncts. If alternation of conjunctions and disjunctions is enforced,Conjoin Disjuncts and Merge Disjuncts can be considered a singleoperation.

Any condition may be specified for a new data measure problem (with noancestor with a data measure). Problems that specialize or generalize adata measure problem may define condition components or operations thatsimilarly modify its condition. Such components or operations may beadded or removed by an authorized user. Navigating to a particular datameasure problem involves additively combining the various inheritedcomponents and operations from various unrelated parents to obtain acondition with which to formulate a single query for that data measureproblem. Where the various operations being combined are commutative,this can be done in a straightforward manner. Conjunctions, for example,may be merged or deleted before or after being embedded in adisjunction. Where a problem has a refinement descendant with multiplerefinement parents, various embodiments must either prevent users fromspecializing the ancestor problem's condition in a way that conflictswith the conditions of other parents of the descendant or accept thatthe child may be made to have an inconsistent condition. Embodiments maythus disallow modifications to a problem's condition where a refinementchild exists, or a refinement descendant has multiple refinementparents, or only where the modification would conflict with otherparents' conditions, or not at all.

Where an entity has multiple data measure parents, its relevant databaseitem set should intuitively be formed by first taking an intersection ofthe set of items of the refined data measures, and then applying anyadditional conditions specific to the particular data measure. It isfrom that set of items that attribute values are extracted. Whengeneralizing a data measure, the relevant set of items should be formedby first taking a union of the set of items of the refining datameasures, and then applying the conditions for the particular datameasure. In each case, the conditions applied are those introduced atthat node or its ancestors (in the logical tree) as modified byspecializing or generalizing conditions. This effect may be simulated byinheriting condition components through either path. The resulting querycan be optimized by the embodiment, directly or by the data source.

An initial example DAG for representing conditions as entitiesassociated with data measures and each other is presented in FIG. 137.It has six data measure problem nodes (80 through 85), represented ascircles, predefined, with 80's condition consisting of a disjunction oftwo conjunctions, the first with two terms and the second with a singleterm. We treat the outer disjunction as implicit (as might be naturalwith DNF), and represent conjunctions with their standard symbol andterms with rectangles containing their content. Lower case lettersrepresent attribute names. Arcs from the term nodes to the conjunctionnodes are labeled with “c” for “construction”. Node 80 is associatedwith the condition ((x≠5)∧(x>3))∨(y=2). FIG. 139 shows data measureproblem 81, refining problem 80, inheriting both conjunctions. If thetwo terms x≠5 and x>3 of the first conjunction are refined to x>6 byapplying Specialize Terms using the first and fifth term refinementrules above, the localized result is as in FIG. 140. Node 81 isassociated with the condition (x>6)∨(y=2). FIG. 141 shows data measureproblem 82, refining problem 81, inheriting the modified conjunctions.If the first (now trivial) conjunction x>6 is dropped by applying RemoveDisjunct, the localized result is as in FIG. 142, with the firstconjunction replaced with a null symbol. Neither the null symbol nor theterm under it would be visible to a user. The condition associated withnode 82 is simply y=2. If instead, we were to refine the condition fornode 83 refining node 80, as in FIG. 143, similar to FIG. 139, butapplied rule Add Conjunct to the second conjunction to create a new termz≠3, the localized result is as in FIG. 144. Node 83 is associated withthe condition ((x≠5)∧(x>3))∨((y=2)∧(z≠3)). FIG. 145 shows data measureproblem 84, refining problem 83, inheriting both conjunctions. If thetwo conjunctions are merged by applying rule Merge Disjuncts, the resultis as in FIG. 147. Node 84 is associated with condition(x≠5)∧(x>3)∧(y=2)∧(z≠3). Finally, data measure problem node 85 refines82 and 84. It is assigned the condition (x>6)∧(y=2)∧(z≠3), a lowerbound, but not greatest lower bound of the conditions of its respectiveparents. We will see that the greatest lower bound,((x≠5)∧(x>3))∨((y=2)∧(z≠3)), may also be attainable.

The result, globally or from node 80 after all of these operations is asin FIG. 146. Arcs between condition nodes are labeled with “R” if theyare considered a restatement of a previous condition for a refining datameasure (using one of the rules above). Note that in removing the firstconjunction from node 82, a null conjunction node is created as arestatement of the first conjunction node with respect to node 82. Notealso that in creating the additional term z≠3 in the second conjunctionfrom node 83, there is an intermediate conjunction node that restatesthe parent conjunction with respect to node 83 and under which the newterm is constructed. Now, navigating to any of nodes 81, 82, 83, 84, or85, using Record Inheritance 2250, similar to that of FIG. 87, gives alocalized DAG substructure as in FIG. 148, FIG. 149, FIG. 150, FIG. 151,or FIG. 152, respectively. Importantly, the condition componentscombined through this process match the ones that resulted from thelocal application of the condition refinement rules. For example, node80 is still associated with the condition ((x≠5)∧(x>3))∨(y=2), which canbe constructed from descendants of 80 labeled only with “c”. The deletedconjunction not available at node 82 is inherited by 85 via 84, so thatthe condition at node 85 remains (x≠5)∧(x>3)∧(y=2)∧(z≠3)

Another initial example DAG is presented in FIG. 154. Here, terms arerepresented simply as subscripted variables and disjunctions arespecified explicitly. Node 90 is associated with the condition(t₀∨t₁∨(t₂∧t₃)∨((t₄∨t₅)∧t₆)). FIG. 156 shows data measure problem 91,refining problem 90, inheriting the full condition expression. If thetwo top-level disjunct terms t₀ and t₁ are “conjoined” to (t₀∧t₁) byapplying Conjoin Disjuncts, the localized result is as in FIG. 157. Ifinstead, we were to specialize the condition for node 92 refining node90, as in FIG. 158, similar to FIG. 156, but applied rule EmbedConjunction with the first conjunction child of the top-leveldisjunction as source and the disjunction child of its secondconjunction child as target, the localized result is as in FIG. 159.Node 92 is associated with the condition (t₀∨t₁∨((t₄∨(t₂∧t₃)∨t₅)∧t₆)).Finally, data measure problem node 93 refines 91 and 92. It is alsoassociated with the condition ((t₀∧t₁)∨((t₄∨(t₂∧t₃)∨t₅)∧t₆)), the GLB ofthe conditions of its two parents.

The result, globally or from node 90 after all of these operations is asin FIG. 160. Arcs between condition nodes are labeled with “R” if theyare considered a restatement of a previous condition for a refining datameasure or with “M” if they indicate a movement of the conditionexpression subtree rooted at the head of the arrow to the node at thetail of the arrow (using one of the rules above). Note that in creatingthe additional conjunction (t₀∧t₁) from node 91, there is anintermediate null term node (invisible to the user) that is restatedwith respect to node 91 by the new conjunction node. Now, navigating tonode 93, using Record Inheritance 2250, similar to that of FIG. 87,gives a localized DAG as in FIG. 162.

While some embodiments may store the additional condition structureresulting from operator applications in the form of the grammarspresented above in this section or a similar one, along with standardrestatement and movement arcs and null nodes as outlined above, otherembodiments may choose to store applications of operators, such as thosepresented above in this section as “Operations for specialization”, moredirectly as condition components with arcs to their operands. In thiscase, condition operator application nodes also point to the problem forwhich they are applied and the semantics of each operator would beimplemented within Record Inheritance 2250. The null node ø can beviewed as a representation of a deletion operator to a single operand.FIG. 161 is an alternate version of FIG. 160 with operator nodes. Anintermediate form would treat movement itself as an operation andinclude three such nodes. Operations could be cascaded by pointing tosuch operator application nodes as operands. Chains of such operatorapplications can be executed by Record Inheritance 2250 to construct anexpression in the chosen grammar. Multiple inheritance of solutions(i.e., relation refinesSolution being many-to-many) would then requirethat an ordering be imposed on the refined solutions, or preferably,that the operator applications for a refining solution not depend on theorder of execution of the operator applications for the refinedsolutions. In the first example above, we have rule Remove Conjunct andrule Merge Disjuncts involving the same node. Somewhatcounterintuitively, when, in integrating these operations as inheritedby node 85, this embodiment merges a deleted conjunction, the newcombined conjunction includes conjuncts of the deleted parent. It is byno means certain that a successful resolution of the conditions of therefined nodes is possible (other than with a condition that is alwaysfalse).

It is possible for embodiments to obtain for nodes that specializemultiple parents, such as 85 in the example specializing nodes 82 and84, a greatest lower bound of the conditions of the refined nodes. Bymarking inherited condition components and operations with the problemnode they related to, embodiments can delete nodes at the condition of aspecializing node only if they were deleted by all parents. Similarly,embodiments can ignore a specialization of a term if it is only by thoseparents that deleted the node.

A consequence of inheriting condition components is that only partialinformation could be available, as described above under “LeveragingInheritance for DAG Exploration” as “not all inherited nodes would beimmediately available to the user”, which may not be acceptable for thispurpose. Any problem with a data measure may need to have its contextsearched for condition definitions during the inheritance process, whichin practice should not be excessive as long as root conditions areidentifiable as such.

If multiple attribute extraction expressions are present, they might bedisplayed separately or combined/aggregated in some fashion. If one ormore of the expressions is typed as a location, the remainingexpressions can be presented in map form, as described below under“General Data Sets” as “Geographic data can be presented on a map”. Ifone of the expressions is typed as a timestamp, the remainingexpressions can be presented via an animation. More generally, if one ormore of the expressions is a continuous quantity, the others can bepresented as plots on a graph with values of those expressions as axes.Quantitative values may be subject to standard aggregations such ascount, sum, average, minimum, and maximum, among others. Theseexpressions can be used to express derived attribute values. Forexample, a problem might involve minimizing the income gap between twodemographic groups. This can be specified and calculated as thedifference between the average income of each group. The results ofevaluating attribute extraction expressions are often best presented astime-based information, with various periodicities.

For embodiments that do not want to count the same items multiple times,only datasets defined at or inherited by the frontier, i.e., the set ofleaves of the substructure or context trees, are relevant foraggregation, and this aggregation should be performed separately for thesubstructure and context trees. Even then, care may be taken to avoiddouble-counting the same items via multiple leaf nodes. If both thecontext and substructure include data measure problems, embodimentsmight calculate and present attribute values related to items indicatedby substructure frontier, items indicated by the context frontier, thedifference between those indicated by the context frontier and thoseindicated by the substructure frontier, or any combination of these.

The question remains of how to combine the attribute values extractedfor data measure parents, especially when they relate to differentattributes. This can be done in various ways including summing ormultiplying if polarities match, subtracting or dividing if they don't.Some form of weighted average may often be appropriate. Weightingcoefficients may be determined automatically to normalize the effects ofthe various attributes on the average (perhaps by maintainingrepresentative attribute values), set explicitly by the user, or somecombination.

Whether storing a full condition with each problem or storing andinheriting condition components, we obtain a condition for each datameasure problem and this is sufficient for providing the data associatedwith any locus node. It is possible to build out the presentationincrementally. Rather than having the client apply Record Inheritance2250 incrementally, for example in going from FIG. 148 to FIG. 149 toFIG. 152 or from FIG. 150 to FIG. 151 to FIG. 152 in the first exampleabove, and then interpret the results, embodiments may arrange to labelthe refinement associations between problems with the differences intheir conditions (expressed as necessary reductions to the selecteditems). This labeling can be performed by the server when a refinementassociation is created. If each data item is labeled with the set ofdisjuncts that it satisfies, then if a term in a particular disjunct isspecialized by a refining problem, upon expanding the substructure so asto reveal that problem, to obtain its data item set, embodiments needonly consider dropping from the parent data item set entities that onlysatisfy that disjunct (although embodiments may recalculate for anyentities that satisfy that disjunct). Similarly, upon contracting thesubstructure so as to hide that problem, embodiments need only considerthat disjunct in deciding which additional entities to include. Dataitems selected for each internal node or attribute extraction resultsmay also be maintained for internal nodes so that they can be restoredquickly on contracting the substructure. Similar notions apply toexploration of the context. FIG. 153 presents a labeled global DAG forthe first condition example. The application of Specialize Terms at node81 leads to a directive to drop all items uniquely reachable from thefirst disjunct unless the new term is not satisfied. The application ofRemove Disjunct at node 82 leads to a directive to drop all itemsuniquely reachable from the first disjunct without qualification. Theapplication of Add Conjuct at node 83 leads to a directive to drop allitems uniquely reachable from the second disjunct unless the new term isnot satisfied. The application of Merge Disjuncts at node 84 forcesembodiments to treat disjuncts as conjuncts, leading to the directive todrop all items not satisfying both disjuncts. Such labeling may bemaintained as conditions of the parent are refined with respect to thechild and, indeed, for other arcs to more general problems when a newone is added (by generalization or by linking existing entities). Whenmultiple parent data measure problems are refined (as with theconstruction of node 85 in the example), each refinement association maybe labeled with sufficient reductions of selected items to ideallyyield, from each data measure problem, their greatest lower bound. Inthe case of additive operators, this may simply involve filling in thoseoperations that are “missing” for any given parent. The reduction on theright corresponding to the application of Add Conjunct for z≠3 is thuscopied to the left, just prior to reaching node 85. Remove Disjunct istreated differently. Since it only appears on the left and not the rightand the disjunct in question was subject to merging on the right, toachieve the GLB condition the conjuncts of the deleted disjunct may beadded back, and since the specialization only relates to the deleteddisjunct, it need not be included. This leads to dropping withoutqualification those items not satisfying both x≠5 and x>3.

These incremental operations could be performed either on the client oron the server, and either in response to user exploration commands or inadvance of them.

As with plans, to create a refinement association between existingproblems, embodiments may verify logical refinement between theirconditions (in the same direction) and perhaps drop any redundantconditions of the refining problem. Others may intend that this linkingmake the conditions of the refined node available to the refining node(as long as they are mutually consistent). The former is moreappropriate to storing full conditions with each problem, the latter tostoring condition components. But where the refined problem has a datameasure and the refining problem defines a new data measure, thesituation is more similar to that of storing full conditions and shouldbe handled as such.

Additional Solution Structure: Plans

Some embodiments may impose ordering on some of the problems motivatedby a solution. They can be considered to be fully unordered, fullyordered, or any nesting of ordered and unordered collections. A simplegrammar is as follows:

-   -   Plan|=ε|MotivatedProblem|‡(PlanList)|∥(PlanList)    -   PlanList|=<Plan,>⁺ Plan

Some such embodiments may imbue additional constraints to reduce thenumber of representations of any imposed ordering. Motivated problemsmight be considered to be unordered, or ordered, or any alternatingnesting of ordered and unordered collections of two or more elements. Agrammar is as follows:

-   -   Plan|=ε|OrderedPlan|UnorderedPlan    -   OrderedPlan|=‡(OrderedPlanArgs)    -   OrderedPlanArgs|=<UnorderedPlanOrLeaf,>⁺ UnorderedPlanOrLeaf    -   OrderedPlanOrLeaf|=OrderedPlan|MotivatedProblem    -   UnorderedPlan|=∥(UnorderedPlanArgs)    -   UnorderedPlanArgs|=<OrderedPlanOrLeaf,>⁺ OrderedPlanOrLeaf    -   UnorderedPlanOrLeaf|=UnorderedPlan|MotivatedProblem        For succinctness, the above grammar is ambiguous. A standard        ordering may also be imposed on UnorderedPlanArgss.

Some such embodiments may allow users to take actions that leave anOrderedPlanArgs or an UnorderedPlanArgs with fewer than two plans,violate the alternation constraint, etc. They might impose simplifyingrules to restore these constraints:

-   -   ‡(Plan)⇒Plan    -   ∥(Plan)⇒Plan    -   ‡( . . . , ‡(OrderedPlanArgs), . . . )⇒‡( . . . ,        OrderedPlanArgs, . . . )    -   ∥( . . . , ∥UnorderedPlanArgs), . . . )⇒∥( . . . ,        UnorderedPlanArgs, . . . )    -   ‡( . . . , ε, . . . )⇒‡( . . . , . . . )    -   ∥( . . . , ε, . . . )⇒∥( . . . , . . . )    -   ∥( . . . , MotivatedProblem₁, . . . , MotivatedProblem₂, . . .        )⇒∥( . . . , MotivatedProblem₂, . . . , . . . )    -   ∥( . . . , MotivatedProblem₂, . . . , MotivatedProblem₁, . . .        )⇒∥( . . . , MotivatedProblem₂, . . . , . . . )

where in the last two rules, MotivatedProblem₂ refinesMotivatedProblem₁. These rules remove singleton collections,nonalternating nested collections, embedded empty plans, and redundantmotivated problems. Additional rules might sort the UnorderedPlanArgsusing the standard ordering as described above.

It should be noted that associating a time estimate with each solutionselected for implementation to solve a MotivatedProblem makes thisstructure capable of representing a Gantt chart and may be displayed assuch.

If a solution has no explicit plan, it is assumed to have anUnorderedPlan of its motivated problems.

If a solution has a plan, for various embodiments a refining solutionwill have a plan at least as specific, e.g., with at least the motivatedproblems of the refined solution and at least the same orderingconstraints, and perhaps more.

There is some similarity between plans and the situation with conditionsdescribed under “Additional Problem Structure: Data Measures”, and manyof the same design options are relevant. Unlike plans, conditions do nothave any ordering. The extensive examples in that section should provideintuition regarding plans.

Plans may be a special kind of solution that refines more generalsolutions, or any solution may have the potential to add a plan.

When refining multiple problems, embodiments may likely check forconsistency of their plans. Plans are inconsistent if one plan requiresa particular motivated problem to precede another and another planrequires that motivated problem to follow the other. When augmenting theDAG with a new solution node that specializes or generalizes existingsolution nodes, an embodiment should ideally provide the GLB or LUBrespectively of the plans of the augmented solution nodes, allowing theuser to edit them to be more or less strict, respectively. The GLB ofmultiple plans will for some embodiments have the union of theirmotivated problems (but dropping more refined motivated problems inplace of motivated problems that refine them) and the union of theordering constraints over those problems. This can be accomplished bycollecting all elements of unordered plans along with the ordered plansthemselves in a single unordered plan. The representation can then beimproved by factoring out common prefixes or suffixes. Thus, given aplan ∥(‡(A,K,X),‡(B,K,Y)), one can obtain ‡(∥(A,B),K,∥(X,Y)), which canbe simplified further if A and B, or X and Y, are in a refinementrelation. Given a plan ∥(‡(A,K,W,X), ‡(B,C,K,Y)), one can obtain ‡(∥(A,‡(B, C)), K, ∥(‡((W,X),Y)). In dropping refined motivated problems inplace of motivated problems that refine them, there is not much harm inperforming the refinement checks locally and incrementally enhancingthem as deferred problem nodes are expanded. The LUB of multiple planswill for some embodiments have the intersection of their motivatedproblems (but dropping refining motivated problems in place of motivatedproblems that they refine) and the intersection of the orderingconstraints over those problems. The above treats unordered plansimplicitly as conjunctions, but some embodiments may gain greaterprecision by supporting explicitly both conjunctions and disjunctions,much as with conditions as described above under “Additional ProblemStructure: Data Measures” as “forming a term for the GLB as X∧X′ or theLUB as X∨X′ . . . ”, but with conjunctions specializing disjunctions andordered plans specializing conjunctions.

One possibility is to store the full plan with each solution, similar tothe situation with conditions above as described above under “AdditionalProblem Structure: Data Measures” as “store the full condition with eachdata measure problem”.

An alternative is to treat plan components as entities, related to eachother and to solutions, and subject to inheritance. Entities may thusinclude ordered and unordered collections and motivated problems.Various kinds of relations might be supported on plan components:component relations, indicating the grammatical structure as suggestedabove; a refinement relation, corresponding tospecialization/generalization of the plan components; a movementrelation, indicating that a subtree is repositioned under a target nodein the refined plan, and an operand relation, a generalization of thecomponent relation indicating that particular plan components can bemanipulated in some way to yield some not clearly identified plancomponent. The plan at a particular solution could be constructed byfollowing its component descendants. All plan refinement associationsshould be considered to be restatements (as described under in-placeiteration), in that inherited refined plans should not be displayed ifthe refining plan is displayed and in that the refining plan need not bedisplayed if it is for an unrelated solution. Some embodiments mayintegrate plan information with the local DAG of which the solution isthe locus. In this case, it may be natural to display restating plancomponents, movement associations, and operator applications that relateto an ancestor or descendant of the locus solution node. Someembodiments may separate the local solution DAG from the local plan DAG,with the latter containing only the components of the plan for the locusof the local solution DAG.

As an implicit GLB is performed upon the plans of approaches that arecollectively refined, specializing operations may be signaled by markersplaced in the structure of plans. Embodiments may provide users withparticular operations for manipulating plans that impose additionalstructure and thus serve to refine the solution:

-   Merge Orderings This can take the form of a user refining inherited    ordered plans (initiating the operation from a base node and    selecting others) in the same unordered plan Unlike in the    corresponding operation Merge Disjuncts for conditions, the user may    provide additional information regarding the relative ordering of    elements from alternative ordered plans. Embodiments might, for    example, allow a user to drag into positions between the elements of    the base node ordered plan, each element of the remaining ordered    plans. In the local DAG, the elements of the selected ordered plans    are moved to their appropriate positions in the base node ordered    plan, avoiding duplicates, and the selected ordered plans removed.    In the global DAG, a new ordered plan restates each of those    inherited ones, so that it can inherit their descendants. A special    form of restatement is required in this case to provide the    additional ordering information, for example the position in the    larger, refining ordered plan of each element of the refined ordered    plan.-   Add Unordered Leaf If the plan structure is empty, replace it with    the given problem. If the plan structure is a MotivatedProblem or an    OrderedPlan, replace it with a new UnorderedPlan containing both    elements. If the plan structure is an UnorderedPlan, simply place    the new term as a construction under its parent in the localized    DAG, but arrange that in the global DAG, the term be placed as a    construction under a new ordered plan that restates the original    with respect to the locus problem. This new ordered plan may operate    over the new term in addition to inheriting the operands of its    parent.-   Specialize Motivated Problem This operation need not be made    explicit as it is already available. The user need merely restate    the motivated problem as inherited by the refining solution.-   Impose Order This operation imposes an ordering on elements of an    UnorderedPlan. A user might initiate this operation after selecting    the children of an unordered plan to order. This can be formulated    as allowing the user to view the existing unordered list and a new,    empty, ordered list, and drag/drop, copying selected elements from    the first list into the second. The elements might be inserted into    the second list in the order copied, or the user might drag them    into particular positions within the new list. Alternatively, the    user might view only the new list with all elements already copied    in, and be permitted to swap or otherwise reorder elements, and to    delete elements. In any case, some embodiments may, in the local    DAG, replace certain elements with a single OrderedPlan of those    elements, which may require simplification. In the global DAG, the    OrderedPlan may be created as a construction under a new    UnorderedPlan that restates the original with respect to the locus    problem (as with AddUnorderedLeaf), and then “movement” arcs created    from the new OrderedPlan up to elements of the UnorderedPlan, to    indicate that they are considered to move back down to the    OrderedPlan. This may be more straightforward for embodiments that    store the locus solution with respect to which the operation is    performed on the movement arc, as suggested parenthetically for    restatement refinements above under “In-place, Iterating DAG    Augmentation” as “storing on each restatement the previously    iterated augmentation upon which it is built”.-   Embed Order This operation takes some existing ordering and pushes    it deeper into the structure. This can be formulated as follows. The    user might select as object an OrderedPlan and then select as target    an UnorderedPlan, both available in the substructure as descendants    of the ordered plan's parent unordered plan (assuming alternation of    ordered and unordered plans, otherwise the nearest unordered plan    ancestor), and with the target not contained within the selected    object. In the local DAG, the object is moved to become a child of    the target. In the global DAG, some embodiments may create a    movement arc between them, pointing to the locus solution. If the    constraints on the target selection are loosened to no longer    require that the target be descended from the UnorderedPlan    positioned as the object's parent, the operation may no longer serve    as a solution refinement.

The latter two operations introduce “movement” arcs, as described aboveunder “Additional Problem Structure: Data Measures” as “movement arcsmay be treated similar to restatements . . . ”.

Corresponding generalization operations would be:

-   Split Ordering The user might require that not elements of an    ordered plan must be ordered with respect to each other, but rather    that various combinations of them must be ordered. This can be    formulated as allowing a user to partition the set of elements of    the ordered plan to be generalized.-   Remove Plan This could be initiated from the plan to be removed.-   Generalize Motivated Problem Restating generalization of problems is    already supported (see “Generalization, Restatements, and    Iteration”).-   Forget Order An ordered plan node immediately under an unordered    plan can be removed. This differs from Remove Plan in that the    ordered elements are not removed, but made into elements of the    ordered plan's parent unordered plan.-   Extract Order An ordered plan within an unordered plan that has an    unordered plan proper ancestor may be moved to be a child of that    unordered plan ancestor.

Embodiments may need to adjust the operations depending on the form ofrepresentation of plans. All operations, however, must serve to make theplan more specific. They must, therefore, preserve any failure ofmotivated problems to meet ordering constraints.

Operations may overlap in their scope to some extent or be restricted toavoid such overlap. For example, embodiments supporting Merge Orderingsmay assume that at least one of the unordered plans being ordered areterms since, if all were ordered plans, applying Impose Order andsimplifying would yield the same result as under that operator, and ifany were unordered plans, one could simplify prior to applying theoperator. Likewise, embodiments supporting Impose Order on ordered plansand simplifying the result need not support Merge Orderings. Ifalternation of ordered and unordered plans is enforced, Impose Order andMerge Orderings can be considered a single operation.

Any plan may be specified for a solution with no ancestor having a plan.Solutions that specialize or generalize a solution with a plan maydefine condition components or operations that similarly modify itsplan. Navigating to a particular solution involves additively combiningthe various inherited components and operations to obtain a plan forthat solution. Where the various operations being combined arecommutative, this can be done in a straightforward manner. Orderedplans, for example, may be merged before or after being embedded in anunordered plan. Where a solution has a refinement descendant withmultiple refinement parents, various embodiments must either preventusers from specializing the ancestor solution's plan in a way thatconflicts with the plans of other parents of the descendant or acceptthat the child may be made to have an inconsistent plan. Embodiments maythus disallow modifications to a solution's plan where a refinementchild exists, or a refinement descendant has multiple refinementparents, or only where the modification would conflict with otherparents' plans, or not at all.

It may be preferred that there be only one way of constructing anygrammar object. This is not an issue for operations at theuser-interface level, so those operations may be more expressive, andtranslated down to the particular operations for manipulating planspresented above in this section. For example, it may be possible throughthe user interface to add a leaf directly to a position in anOrderedPlanArgs.

While some embodiments may store the additional plan structure resultingfrom operator applications in the form of the grammars presented abovein this section or a similar one, along with standard restatement andmovement arcs and null nodes as outlined above, other embodiments maychoose to store applications of operators, such as those presented abovein this section as “particular operations for manipulating plans”, moredirectly as plan components with arcs to their operands. In this case,plan operator application nodes also point to the solution for whichthey are applied and the semantics of each operator would be implementedwithin Record Inheritance 2250. The null node ø can be viewed as arepresentation of a deletion operator to a single operand. Operationscould be cascaded by pointing to such operator application nodes asoperands. Chains of such inherited operator applications can be executedby Record Inheritance 2250 to construct an expression in the chosengrammar. Multiple inheritance of solutions (i.e., relationrefinesSolution being many-to-many) would then require that an orderingbe imposed on the refined solutions, or preferably, that the operatorapplications for a refining solution not depend on the order ofexecution of the operator applications for the refined solutions. Someembodiments may find that standardizing the ordering ofUnorderedPlanArgs is helpful in accomplishing this. It is by no meanscertain that a successful resolution of the plans of the refined nodesis possible. To take a simple case, where alternate branches imposedifferent orderings on a two-element unordered plan, they cannot bemerged.

A consequence of inheriting plan components is that only partialinformation could be available, as described above under “LeveragingInheritance for DAG Exploration” as “not all inherited nodes would beimmediately available to the user”, which is likely not acceptable forthis purpose. Any solution with a plan may need to have its contextsearched for plan definitions during the inheritance process, which inpractice should not be excessive as long as root plans are identifiableas such.

Embodiments supporting solution refinement may require that the allrefining solutions' structure be consistent with that of the refinedsolutions. If a refining solution already imposes structure thatduplicates that being added for the refined solution, the refiningstructure can be deleted as superfluous, or it can remain to becomeeffective if the structure is ever removed from the refined solution. Ifa refining solution already imposes structure that is inconsistent withthat being added for the refined solution, the operation may beprohibited or the refining solution may be disassociated from therefined solution (and any intermediate descendants) and considered torefine any parents of those refined solutions.

Other Topics

Supporting Social Innovation

Invitations and Applications to Connect

Project augmentations performed on a project create “strong”associations between the new entity and the old one. The suggestion isassumed to be made available to the administrator of the augmentedproject, although the contributor may or may not be given anadministrative role over the new project in this process.

Some embodiments may also support “weak” associations between existingprojects. These can use the mechanisms described above under “DAGRefinement of Existing Entities” as “adding a refinement associationwith respect to a cross-kind augmentation”. A checked-in projectadministrator may have options (e.g., via their context menu) to invitea more specific project (based on the project content) to refine it orto apply to refine a more general project (again based on the projectcontent). Crucially, such weak refinements are capable of supportinginheritance of solutions or other project content.

These variations in strength of association may relate not only toprojects but other kinds of entities as well. Embodiments may, forexample, support strong “refinement” associations between users withinan organization, representing for example reporting relationships ormentoring, and weak associations between users between organizations,representing for example mentoring only.

The system can recommend (as under “Recommendations”) entities forconsideration for weak associations.

In some contexts, a project administrator or other user may benefit froma “birds-eye” view of the connections between organizations. Areas oforganizational activity can be highlighted by focusing on the weak linksbetween organizations and condensing sequences of strong links Suchregions can additionally or alternatively be labeled with theorganization and/or coded by color or other visual attribute and/or havea border mark an organizational boundary between entities associatedwith different organizations. Entities inherited from anotherorganization could then appear as “islands” within the region of theinheriting organization.

This functionality may leverage functionality already described tosupport sharing between organizations. Here, though, a second form ofrelation is introduced, and embodiments need to be aware of which theyare traversing. The server, in creating an “ecosystem” DAG, can, forexample, skip over all strong links from the locus nodes except thoseleading to nodes with a weak link to other projects. Then, likewise, itcan continue condensing to any subsequent weak links. Such “skipping”should take place when considering parent or child entities in ReduceDAG 0210 and Record Inheritance 2250. These ecosystem-oriented DAGs canbe passed to the client along with the standard DAGs.

In some contexts, only entities related via strong associations may bevisible. In others, entities related via any association may be visible.Embodiments may include entities connected by weak links and/or entitiesinherited through weak links in the standard DAG as well as theecosystem DAG, or only in the ecosystem DAG. If the former, the user maybe able to control visibility of entities connected by weak links in thestandard DAG via options similar to those described under “DAGFiltering”.

FIG. 163 through FIG. 171 present an example of this functionality. FIG.163 shows a project screen for a problem “How can we establishself-sufficiency among people?”, with a single solution listed, “Let'steach them to run businesses!”. FIG. 164 shows a user screen for anotherproblem, “How can we establish self-sufficiency among single mothers?”,created by a different user, Joanna Doe, who has checked in asadministrator (a relevant example of check-ins involving FIG. 229through FIG. 231 is presented below under “Project Check-ins”). FIG. 165shows Joanna navigating to the first project screen and applying tospecialize that challenge with her own. After her application isaccepted (via the online system or link in an email), the view from thedependencies tab of her project screen will for this embodiment be as inFIG. 166, with the new generalizing problem in the context and itssolution inherited into the substructure. Joanna jumps on this idea, andbuilds out the structure as in FIG. 167, culminating with “How can weestablish connection among single mothers starting businesses?”. Now,another individual, Jessica, has begun considering a broader problem,“How can we establish connection among single mothers with commoninterests?”. FIG. 168 shows her user screen, with her checked in asadministrator. In FIG. 169, we have Jessica's project inviting Joanna'sto specialize it. After the invitation is accepted, FIG. 170 shows thedependencies tab for the specializing problem, with the context reachingout to one and eventually the other external generalizing problem. Theview from the ecosystem tab is in FIG. 171. Notice that only theentities bordering on other organizations appear. Other embodimentsmight indicate where intermediate entities have been elided. Here, theregions corresponding to the same organization are coded with the samecolor.

Recommendations

The system can recommend projects to users, users to projects, projectsto each other (problems to problems and solutions to solutions), or (inthe case of user associations representing mentorship) users to eachother. A recommendation to a project would be shown to an administratorof that project when they are checked-in to the project.

Consider first, as an example, recommending projects to people (for aparticular role). This can be done by finding similar projects, thenconsidering who they have in that role. It can also be done by seeingwho else this project has in that role (if anybody) and then findingsimilar people. Embodiments might make use of both sources ofrecommendations, as well as those obtained by applying the similaritymatrices for both the project and the individual. The situation issimilar for recommending an entity of any kind₂ to an entity of kind₁(where they may be the same kind). If they are in fact the same kind,then embodiments may consider directional refinement relationships (thedirection depending on the direction for which we want to recommend) inplace of the cross-kind relationship. This process is presented in FIG.172. Some embodiments, though, might simply recommend similar entitiesif both kinds are the same.

Rather than selecting from the three methods just mentioned for buildinga ranked list of projects, some embodiments may apply all three andapply an initially arbitrary weighting based on which method was used(presumably penalizing the application of both similarity matrices),prior to merging the results.

Rather than restricting to just one role, it is possible to considerother roles as well, each likewise with a lower (but otherwisearbitrary) weighting.

Especially in the case of search results, but for recommendations aswell, once the results list is obtained, there may be benefit infiltering out lower-ranked projects related by refinement.

Otherwise, the suggested procedure is relatively standard, with a fewenhancements. In either method above, finding similar entities involvesbuilding a vector and applying a similarity matrix. A similarity matrixis a mapping from a pair of entities of the same kind that returns anestimate of how similar they are. Consider users similar if they havesimilar biographies or contribute to similar projects. Consider projectssimilar if they have similar names or descriptions or are contributed toby similar users. It may be useful to represent similarity matricesusing a vector of data structures such as balanced trees that supportretrieving an ordered list of similar entities from any given entity.

The similarity matrices may be constructed from feature vectors that canbe generated for each entity. Let each similarity matrix cell value be ameasure of the similarity between positive occurrences in featurevectors that both filtered and are adjusted by “surprise” value (so wewant to recommend the most surprisingly similar projects), calculated asa dotted product divided by the product of the square roots of thenumber of non-zero entries in each. This calculation over featurevectors corresponds to the cosine of the angle between the two vectorsand is a standard distance measure. Surprise value can be measured as aTF.IDF score. The only modification to standard practice there istreating it as a linear adjustment in addition to as a threshold.

For a problem or solution, the features can be words, required skills(problems do not have required skills, but as described below we canconsider related solutions), contributors, and behaviors. For a user,the features can be words, skill proficiencies, projects contributed to,and behaviors. The surprise element corresponds to how rarely thefeature values occur.

The value in the feature vector of a word feature for a project is ameasure of how often (at what rate) it appears in the name anddescription and in the names and descriptions of ancestor and descendantprojects, all relative to its rate of appearance in general usage oracross the server database, with weighting factors for, for example,name versus description and each of several levels of ancestor anddescendants that again, are initially arbitrary, but read from a file.Later, a higher-level process can fine-tune the weighting factors bytesting the recommender with modified values. The value of a contributorfeature for a project is the role (if any) of the contributor on theproject or on ancestor or descendant projects, adjusted by the scarcityof that contributor having such a role, or any role, on any projects,and again with weighting factors for each of several levels of ancestorsand descendants. The value of a skill feature is calculated similarly toa contributor feature (without any notion of role).

The values of user features would be calculated similarly.

This approach incorporates collaborative filtering as well ascontent-based recommendations.

We can improve recommendation quality by, for example for projects,saying that the contributor feature is the role (if any) of thecontributor or similar contributors on the project, along with degree ofsimilarity. Note that the definitions are then circular, but we can usedynamic programming to calculate entity features incrementally.

Features can also include system behaviors, calculated by how common andrecent they are for that entity.

As system behaviors take place, the feature vectors and similaritymatrices should be recalculated incrementally.

Similarity matrices are generally symmetric, but some embodiments couldgeneralize them to distinguish based on the direction of recommendation.

In the particular case of recommending people and solutions to eachother, embodiments may restrict recommendations to users and solutionssuch that the users have sufficient skills to qualify for therequirements of the solution. Although some correspondence is certainlyappropriate, this filtering may not be appropriate, since, generallyspeaking, the skill requirements of a solution can be met by acombination of users. For embodiments where skill requirements are tiedto resource requirements (as described below under “Resources” as “skillrequirements may be associated . . . with . . . human resourcerequirements”), recommendations could be modified to recommendindividuals to resource requirements, the feature vector of which wouldshare much with the vector of the underlying solution but might alsoreflect, for example, the presence of words in a resource requirementdescription.

In including skills of dependent projects in the feature vectors ofusers and projects, we enable the tuning of weighting factors inrecommendation algorithm to prefer recommendations of individuals tohigher-level projects who are proficient not just in the skills requiredby that project, but in the refining skills required by multipledependent lower-level projects.

Secondary DAGs

Embodiments may distinguish between a primary localized DAG, providinginformation about ancestors and descendants of the node or nodes towhich the user has navigated, and secondary DAGs, providing perhaps morelimited information about the ancestors and descendants of entitiesrelated to any entity represented in the primary DAG. Such embodimentsmight store lists of references to directly related entities with eachentity in the primary localized DAG. These references could be used bythe client to access the secondary DAGs (also provided by the server),entities of which would be related by a refinement relation.

The server could use a multiple-entity extension of Reduce DAG 0210 asdiscussed above under “Multiple Cross-kind Augmentation” as “Dag_(E)|¹”to build a secondary DAG of entities related by various selectedrelations to entities related by the appropriate cross-kind relation tothe locus entities of the primary DAG, to which the user has navigated.

A basic approach is to have the secondary DAG include nodes reachable byrefinement from its locus nodes, which are set to those associated bythe cross-kind relation with the locus nodes of the primary DAG.

Embodiments may wish to display the secondary DAGs based on what portionof the primary DAG is open, as a form of aggregation, as described under“A Method for Exploration of Hierarchical Structures and Representationof Context Thereof”. Active, overall, and constituent aggregations couldbe maintained.

One way of achieving this is to have the secondary DAG include nodesreachable by refinement from its locus nodes, which are set to thoseassociated by the cross-kind relation with not just the locus nodes ofthe primary DAG, but all nodes currently visible in the primary DAG. Asthe primary DAG is expanded, locus nodes are added to the secondary DAGand as it is contracted they are removed.

This could be implemented by the server sending the full secondary DAG(assuming full expansion of the primary DAG) to the client, which wouldbe responsible for incrementally localizing it to the state of expansionof the primary DAG. Thus, the client would modify both the secondarylocal DAGs and its associated visual presentation

More scalably, the client could request additional subDAGs as necessary.To avoid resending common portions of the DAG multiple times, the servercould track which nodes and edges were already transmitted.

Another way of displaying the secondary DAGs based on what portion ofthe primary DAG is open is to have the secondary DAG show refinementconnections between entities related to those represented in the primaryDAG. Locus nodes of the secondary DAG are fixed as entities related bythe appropriate cross-kind relation to the locus nodes of the primaryDAG. As the primary DAG is explored, entities accessible in thesecondary DAG grow and shrink such that they include the entitiesrelated to those open in the primary DAG. This can be implemented byplacing a binary indicator on each element of the secondary DAGexpressing whether or not it is currently accessible, and onlyconsidering accessible nodes in determining the children of a node in alogical tree.

As primary DAG folders are opened, embodiments might augment theaccessible portion of the active secondary DAG with entities related tothose just revealed, but not already accessible in the secondary DAG.But as primary DAG folders are closed, an embodiment would not knowwhether the entities related to those being hidden are also referred toby other entities still visible, so it might need to recompute theaccessible portions of the secondary DAG.

To handle this efficiently, embodiments might maintain, for eachsecondary entity, primary entities to which it is related by theappropriate relation. As primary DAG folders are closed, retract fromthe accessible portion of the secondary DAG information about relatedentities no longer accessible via direct associations from remainingopen primary DAG nodes.

For example, consider that various solutions require skills, formalizedabove under “Project Management Entities and Relationships IncludingSeparation of Problem and Solution Spaces” as directlyRequiredBy. Suchskills might themselves be related by a subskill relation (formalized asrefinesSkill), with more general solutions requiring more generalskills. Rather than (or in addition to) showing those skills as part ofprimary project DAG, embodiments may present a secondary DAGhighlighting those skills required by solutions that are open in theprimary DAG, either by restricting the secondary DAG to those entitiesor by treating those entities as locus nodes.

As another example, if the primary DAG is representing theorganizational hierarchy, one could view the skill proficiencies withinvarious regions of the hierarchy and explore the subskill relationshipsamong them. Or conversely, if the primary DAG is representing the skillhierarchy, for the skills within various regions of the hierarchy onecould view either projects requiring those skills or users proficient inthose skills and explore relationships among them.

Resources

Embodiments may associate types of resource requirements with solutions.Resources may be human, bureaucratic, or of other customizable kindssuch as equipment, computer software, or chemical or biologicalsolutions. Embodiments may support the assignment (allocation) ofresources to a solution in order to address its requirements.

A user may then be assigned to a solution as a human resource. For suchembodiments, the assigned user would take on the role a collaborator.Cash can be considered a resource, as provided by donors or investors(described below under “Contributions and Disbursements” as “Someembodiments may support contribution of funds”) and transferred within aproject (as described under “Budgeting Support”).

For embodiments only supporting human resources (as opposed to otherresources), the kind of resource may be implicit and only the number ofpositions relevant. For many embodiments, skill requirements may serveas a resource type for human resources. In this case, skill requirementsmay be associated, not with an entire solution as described above, butwith each of its human resource requirements. For a computer program,resource requirements may take the form of a type, UML diagram, or otherprogram specification. Types of molecular resources may take the form ofa condensed formula (chemical formula), including non-stoichiometricformula and notations for repeating units in polymer and charge on ions;various forms of structural formula (molecular graphs), including Lewisstructures, skeletal formula, and stereochemical formula; molecularorbital diagrams (valency interaction formula), etc. Or building onthese, they might include solutions containing various components inparticular concentration ranges.

Resource requirements could be specified as a bag, e.g., as a set ofresource types, each tagged with the quantity required. For humanresource requirements, the quantity might be in units of full-timeequivalents (FTEs).

A refinement of a solution may have resource requirements that extend orspecialize those of the refined solution. In the case of a humanresource requirement, a refining solution may require a human resourcewith additional skills (not required for the refined solution),subskills of those skills required for the refined solution, and/orskills at greater proficiency than required for the refined solution.UML diagrams could be specialized, for example, with additionalsubclasses or methods. Less explicit molecular specifications could bespecialized by consistent, more explicit specifications.

Resources allocated to a solution may be allocated in turn tolower-level solutions, e.g., solutions of component problems, or theirlower-level solutions (perhaps only those that have been selected forimplementation, as described below under “Associating a StateMachine/Bayesian Network With Each Node in a Refinement Hierarchy” as“selected for implementation”) addressing the problems motivated by thatsolution. If plans are supported as under “Additional SolutionStructure: Plans”, then the initial assignment of resources may beconstrained such that the same resource can be assigned to solutions ofproblems that must be addressed in sequence, but not to those that maybe addressed in parallel. Once a solution is completed (as describedbelow under “Associating a State Machine/Bayesian Network With Each Nodein a Refinement Hierarchy” as “completed”), however, its resources arereleased for assignment to other solutions.

Embodiments may, however, support declaration of some resource types asconsumable, such that those resources would not be released aftercompletion of solution implementation. While software programs aregenerally not considered consumable, chemical or biological solutionsmay well be. Consumable resources can be used to represent resourcetransformations that may occur in the process of implementing solutions.Experience gained by project collaborators during solutionimplementation could even be represented as an increase in the skills ofthose human resources.

The process of allocating resources from higher-level to lower-levelsolutions can be automated somewhat by embodiments that supportassociating a resource requirement of a higher-level solution with aconsistent and potentially more general resource requirement of asolution to a component problem of that higher-level solution, toindicate that the resource should be made available for implementingthat solution.

Resource requirement types and available resource types can be presentedas auxiliary project information, as described under “AuxiliaryInformation and Aggregations”. The collective resource requirements of asolution with a plan can be calculated by an embodiment from thestructure of that plan. Embodiments might distinguish the idealrequirements, which would allow all parallel operations to occursimultaneously, with the minimal requirements, which would in some casesforce an ordering even among parallel components due to resourcebottlenecks. In either case, the resource requirements of componentproblems in a sequence might be calculated as the GLB of therequirements of the solutions to those problems, e.g., resource typesspecifying the least requirements capable of satisfying the selected(for implementation) solutions of each sequent plan. The minimalresource requirements of component problems in parallel might likewisebe calculated as the GLB of the requirements of the selected solutionsto those problems, while the ideal requirements might be calculated asthe sum of the requirements of the selected solutions to those problems,e.g., resource types specifying all of the selected solutions of eachdisjunct plan. The first calculation could separate connected componentsin the DAG of required resource types and their refinement relation,make each a required resource with type equal to the GLB of the requiredresource types in the full resource type hierarchy, but this might betoo exacting. Instead, some embodiments would separate chains of related(by refinement) resource types and make each a required resource withtype the lowermost element of that chain. The second calculation (idealrequirements for components in parallel) could be calculated by taking abag union of the disjunct resource requirements, summing the quantitiesfor identical resource types. If a solution has no plan, paralleltreatment of the component problems is assumed.

In setting the resource requirements of a solution, embodiments mightrequire at least sufficient resources to satisfy the solution's plan.

Embodiments may also associate resource types (for some embodiments asingle resource type) with a problem to indicate, for example, theexpectation that a solution to the problem will generate thoseresources. In this case, the completion of any solution to that problemcan be assumed to generate a resource with the associated type. If theproblem exists as a step in a sequence (including multiple nestedsequences), then the generated resource can be made available forassignment to solutions of subsequent problems. Thus, the resource typesof component problems of solutions to a larger problem can be viewed asspecifications of intermediate results in generating the resource whosetype is associated with that larger problem. Embodiments may supportassociating a resource generation expectation of a component problem ofa solution to a higher-level problem with a consistent and potentiallymore general resource generation expectation of that higher-levelproblem, to indicate, for example, that the resource will be madeavailable for satisfying the higher-level problem's resource generationexpectation.

Similarly, embodiments may support associating a generated resource typeof a component problem of a solution with a consistent and potentiallymore general resource requirement type of a solution to a subsequentcomponent problem. In this case, the generated resources would need tobe taken into account in limiting the total resources required, ascalculated above in this section as “The collective resourcerequirements of a solution with a plan can be calculated . . . ”. Inparticular, the requirements could be signed, with (arbitrarily)negative requirements corresponding to resource generation expectationsexceeding resource requirements. Calculation of resource requirements ofsequences would be potentially reduced to multiple binary calculations,with any resource generation expectations serving to eliminate anyrequirements that they might satisfy, or else are recorded as negativerequirements that can be carried forward to reduce subsequent resourcerequirements. Calculation of minimal requirements of parallel planswould be as before, except that the resource requirements would besigned with no cancellation allowed. In calculation of idealrequirements of parallel plans, an ordering should be imposed thatdelays disjunct plans with requirements that might be satisfied byresource generation expectations of other disjunct plans.

Some embodiments may declare that each of some or all resourcerequirements of a solution and resources expected to be generated for aproblem present one additional problem for their installation andanother for their dismantling (although dismantling may be trivial oromitted), with these problems determined at least in part by the type ofresource involved. Installation of a human resource may involve hiringand/or training. Installation of a software resource may involveprogramming and/or configuration. Molecular resources may be produced byparticular chemical reactions. Until resources are assigned andinstalled, solutions of the motivated problems are not implementable.Until resources are dismantled, solutions of the motivated problems arenot completed. Other embodiments may require such installation anddismantling problems to be specified explicitly as any other componentproblems of the higher-level solution.

Adding Assumptions

In a twist on generalization, it is often the case that one notices thata solution is not quite as general as presented, in other words thatthere are unmentioned assumptions of the problem that it claims tosolve. Embodiments may allow a user to identify assumptions of asolution, which can be treated as refinements of the problem that itaddresses, such that after the operation, the solution is made to solvethe refined problem.

Mutually Exclusive Refinements

In some cases, two or more specializations are independent and thuspotentially overlapping in scope. In others, they are orthogonal andthus discrete. For example, specializations of a problem by distinctgeographic areas could safely be considered mutually exclusive. Bysupporting the user in specifying such relationships, it is possible torestrict the inheritance of, taking problems and solutions for example,a solution to the parent problem that refines one of the mutuallyexclusive siblings solutions by any other such sibling, as is suggestedmore generally above under “In-place, Iterating DAG Augmentation” as“restatements can also form a basis for controlling access”. It is alsopossible to support mutually exclusive refinements of solutions, skills,etc. Some embodiments may provide a mechanism for marking an entity suchthat all lower-level refinements of the same kind are mutuallyexclusive.

Strict Refinement Embodiments

Some embodiments may differ from the presentation above in requiringthat substructures of various types of refining nodes be obtainable onlyby inheritance or refinement from substructures of the refined nodes andprohibit such substructures from being introduced directly into therefining nodes. In particular, having any problems motivated by refiningsolutions refine problems motivated by refined solutions leads to anotion of solution refinement closer to that of theoretical computerscience, as opposed to the approach presented above, which is moresimilar to the way classes are extended in modern programming languages.It is also possible to have any solutions addressing refining problemsrefine solutions addressing refined problems.

Associating a State Machine/Bayesian Network with Each Node in aRefinement Hierarchy

One might consider a state machine representation of solution status,with states for the various possible status values, corresponding toeither the level of development of solution implementation or the levelof authorization for proceeding with such implementation. For example,classic status values for software project iterations includerequirements analysis, design, coding, and system testing. Status valuesfor authorization could include various stages of approvals orevaluations of feasibility. These could be represented in separate statemachines or a single state machine. A general list of statuses would be“open”, “not being considered”, “selected for implementation”, andwithin the latter, “not yet started”, “resources being developed”,“being implemented”, “resources being dismantled”, and “completed”.

Given a state of implementation/approvals that a solution hasexperienced, one can consider the probability of various additionalprocesses that might be applied next to lead to a new status. Machinelearning approaches can be used to impose a graph structure onstatistical data concerning how solutions progress from one status toanother. Such statistical data can take into account variouscharacteristics of the problem or solution. One such approach is that ofRebane, G. & Pearl, J., “The Recovery of Causal Poly-trees fromStatistical Data”, in Proceedings, 3rd Workshop on Uncertainty in AI,(Seattle, Wash.) pages 222-228, 1987. Such approaches are among ways of“training” the network to offer appropriate transitions among states.

A network that has been trained for solutions with particularcharacteristics may be used as a starting point for solutions with morespecific subcharacteristics, e.g., solutions that receive values forparticular attributes that specialize those for which the network wastrained. Such networks can then evolve separately.

Similar techniques can be applied to problems, if they are to pass amongvarious statuses.

Our refinement hierarchies of problems and solutions can be used as aframework for organizing various state machines defining how eachsolution in the hierarchy is to pass from one status to another. Statemachines associated with problems can apply to all solutions thataddress those problems. As one descends a refinement hierarchy ofproblems, training data may be segregated between various child problemsat each level, and thus a different state machine derived. Learning canthus be propagated downward through the refinement hierarchy.

Training data may take the form of asking users what next status isappropriate for a given solution. Alternatively, it might take the formof asking users what previous status would have been appropriate for agiven solution (for example, that a prototype should have been reviewedby potential users).

Regardless of the time direction for which appropriate transition datais collected, embodiments may choose to also ask why the suggested statetransition is or would have been appropriate. The answer could be thebasis of a signal that could trigger a transition in a revised statemachine (for example, because the implementation effort was projected torequire more than 40 man-hours).

Information can potentially also be propagated upward through thehierarchy. For example, if a transition is found to be appropriate forsolutions of a given problem, embodiments might ask sibling problems(under any parent) about whether the transition is appropriate there aswell (this might require also establishing certain states in the siblingproblems). If the transition continues to be appropriate for solutionsof sibling problems, we can suggest it for solutions to that parentproblem. This strategy can be used for propagating any learning upwardthrough a refinement hierarchy, not just related to problem hierarchiesor state machines.

Alternatively, state machines of refining problems can override those ofthe refined problem by any other means, such as explicit editing by aproject administrator.

Moreover, the hierarchy of solutions can be associated with ahierarchical state machine, with hierarchically nested states whereby asolution in a nested state is also in the surrounding states.

Such hierarchical state machines may be applied such that more deeplynested states that apply to a solution get first chance to define howvarious input signals (such as successes or failures in authorization,implementation, testing, budget, etc.) are handled.

Alternatively, and preferably, hierarchical state machines may beapplied such that new signals relate to deeper levels of hierarchy, andthat those new signals determine transitions between substates of thestate at the higher level.

Since the problem and solution hierarchies are closely related (e.g., bythe correspondence constraints under “Explicit DAG Augmentation bySpecialization/Multiple simultaneous refinement” and “DAGGeneralization”), refined solutions would naturally be subject to thestate machine modifications imposed by refined problems. For consistencyand continuity, some embodiments may thus restrict state machinemodifications for refining problems to impose additional lower layers ofdetail on states that exist for the refined problem.

Because state machines and additional layers of state machines can beadded while solutions exist, a state machine at any level should have adesignated default start state. Any new or existing solutions are placedin the default start state at the top level machine, or at a lower levelmachine when they enter the appropriate state at the higher level. Noend state is needed, but any number of end states can be created bybeing defined with no outgoing arcs.

Any particular solution can be transitioned between states via the userinterface, or particular transitions can be associated with rules thatare applied automatically. Managerial approvals or disapprovals would beappropriate for the former treatment, while solutions being over-budgetor past deadline would be examples of candidates for the latter.

FIG. 173 shows a possible user interface for associating state machineswith problems. The context menu for a problem, in addition to optionsfor editing or augmenting the entity, contains an option for “View statemachine”. Selecting this option might bring up a diagram of the currentstate machine for the problem. Here, we have various states, includingone identified as “Implementation over-budget” which is attained via atransition “Grant additional funds”. Two outgoing transitions arelabeled “Grant additional funds” and “Suspend project implementation”.From any given state, a context menu includes an option for “Decomposestate” which, when selected, displays a lower-level state machine(creating one if it did not already exist). Context menu options forindividual nodes support editing the state label, removing the state andadding an outgoing state transition. A state-independent context menusupports adding a new state, setting the default state, or bringing up awindow with the next higher level state machine.

FIG. 174 shows a possible user interface for associating state machineswith problems. The context menu for a solution, in addition to optionsfor editing or augmenting the entity, contains an option for “Viewcurrent state”. Here, a two-level state is displayed, the upper levelbeing “Cleared for implementation” and the lower-level state being“Implementation over-budget”. Another option, “Apply state transition”provides another context menu with transitions available for this nodefrom various levels of the state machine as options. An additionaloption from the solution-level context menu “Recommend next/previousstate” allows for obtaining input regarding how a solution should orshould have been handled and why. Although this is presented here as auser option, embodiments may prefer to randomize this process to avoidbias through self-selection.

A Method for Exploration of Hierarchical Structures and Representationof Context Thereof

The general approach is as follows. Present a portion of a DAG as atree. Then repeatedly allow the user to take either of the followingactions:

Expand the Subtree at any Node on the Closed Frontier of the DAG

-   -   Doing so should both automatically close any previously open        subtrees that “conflict” with the subtree being opened, e.g.,        any child of the node being opened that is already visible at        another node of the DAG should be hidden; and open some        descendants of the node being expanded.        Collapse the Subtree at any Node Strictly within the Closed        Frontier of the DAG    -   Doing so should hide any strict descendants of the node being        collapsed, and the node being collapsed should be closed.        Various embodiments may accomplish this using some combination        of strategies, as described below.        Related sets of strategies deal with how much of the DAG should        be initially visible, and how much revealed when a node is        expanded.

Because embodiments may choose to constrain the tree such that only onenode associated with any given entity may be visible, we call two nodesthat are associated with the same entity directly conflicting. To hide anode, embodiments may collapse its parent. All but the final twostrategies listed may not be appropriate where the number of descendantsof a node is not finite.

First, we present various Initialization Strategies. All of them preventmultiple directly conflicting nodes from being displayed.

-   -   Initialization Strategy #1: Open as much of the DAG as possible        until opening another node would reveal a child node that        conflicts with a visible node; do not open these nodes. The        children of a node can be expanded in any order. At most one        conflicting node is visible.    -   Initialization Strategy #2: Open as much of the DAG as possible        until an entity can be reached by more than one parent node; in        this case do not open any such parent node. No conflicting nodes        are visible.    -   Initialization Strategy #3: Continue to open nodes as long as        there is only one nonleaf child.    -   Initialization Strategy #4: Continue to open nodes as long as        there is only one child.    -   Initialization Strategy #5: Open only the locus node(s).    -   Initialization Strategy #6: Do not initially open any nodes.

Next, we present various Explicit Node Expansion Strategies. Here,embodiments may open the requested node; how much additional is to beopened, however, may vary. To maintain the constraint prohibitingdisplay of multiple directly conflicting nodes, embodiments may hidesome nodes, although the amount of hiding needed may depend on therestrictiveness of the expansion (unfolding) strategy. Only the finalstrategy listed may be appropriate where the number of descendants of anode is not finite.

-   -   Explicit Node Expansion Strategy #1: Hide any nodes that        directly conflict with children of the node being expanded, then        open as much of the DAG as possible until opening another node        would reveal a child node that conflicts with a visible node; do        not open these nodes. The children of a node can be expanded in        any order. At most one conflicting node is made visible.    -   Explicit Node Expansion Strategy #2: Hide any nodes that        directly conflict with children of the node being expanded, then        open as much of the DAG as possible until an entity would be        revealed that can be reached by more than one path; do not open        these nodes. The children of a node can be expanded in any        order. No conflicting nodes are made visible, other than        children of the one for which expansion was requested.    -   Explicit Node Expansion Strategy #3: Close any siblings and        continue to open nodes as long as there is only one nonleaf        child.    -   Explicit Node Expansion Strategy #4: Close any siblings and        continue to open nodes as long as there is only one child.    -   Explicit Node Expansion Strategy #5: Only open nodes as        explicitly directed. Variations exist based on how much of the        tree to hide prior to opening the node: hide any visible nodes        associated with the same entity as each revealed node or close        any siblings.        Various embodiments use related strategies for both        initialization and expansion, but some embodiments use different        strategies in these cases, or in any sub-cases as they see fit.

Reopening Strategies deal with how to react when a subtree that has beenclosed is reopened.

Reopening Strategy #1: Some embodiments may reopen that subtree to itsinitial position.

Reopening Strategy #2: Others may reopen it to the same position that itwas in prior to being closed.

Embodiments may exhibit subtle differences in how they deal with logicalleaf nodes. Some embodiments may choose to allow leaf nodes to be openedand closed in spite of the fact that there are no children to display.These embodiments may use a single binary variable on nodes to representwhether they are open or closed. They may, as an optimization, use aseparate binary variable to represent directly whether a or not a nodehas children. Other embodiments may track whether nodes with childrenare open or closed, and for leaves not maintain this information. Again,whether a node is a logical leaf or not can be maintained explicitly ordetermined by counting its logical children. We assume that expansion,collapse and the various strategies for unfolding only take place onnodes with logical children, although these checks are omitted from thefigures.

A pair of strategies reflects the lifetime of tree nodes.

-   -   Static Lifetime Strategy: Some embodiments may initially        construct the entire substructure (or context) from the DAG as a        single (possibly inverted) tree in which certain entities may be        represented multiple times, and then adjust which nodes are to        be displayed in accordance with a selection of the above        strategies (such that any entity is displayed at only one node        at any time). Depending on the situation in which the        exploration takes place, an embodiment may explicitly hide and        show nodes exclusively, or leverage underlying technology such        as a browser to set these attributes in some circumstances.    -   Dynamic Lifetime Strategy: Other embodiments may reconstruct        nodes from the DAG each time they are to be displayed, and        delete them when they are to be hidden.        Presentation of DAG Substructure as a Tree        Here the tree grows downward and its purpose is to allow the        user to explore descendants of a node, i.e., its substructure.

The approach for the representation of a DAG as a tree is shown in FIG.175 for a particular DAG under navigation. The tree structure (ofpossible snapshots into the DAG) corresponds exactly to the DAGstructure, with children of an open node (marked with “o:”) indented andbelow that node.

Embodiments implementing the Static Lifetime Strategy may or may notmake use of a convention that if a node is hidden, all of itsdescendants can be inferred to be hidden as well without explicitlymaintaining that fact for each descendant.

We now describe each operation for the Static Lifetime Strategy. FIG.176 and FIG. 177 describe the two parts of the set-up process. FIG. 176shows that Static Substructure Construction 111100 iterativelyconstructs the substructure, starting with the locus node anddiscovering descendants. No order is specified between construction ofthe various nodes, but if pointers are maintained in either direction,it may be convenient to construct the referenced node prior to settingthe pointer on the node that references it. If pointers are maintainedin both directions, the order may be arbitrary as one of the pointersmay need to be set after both nodes have been allocated. FIG. 177 showsthat Static Substructure Initialization 111101 both makes the locus nodevisible and applies an Initialization Strategy. For InitializationStrategy #6, expansion simply collapses the locusNode but for otherInitialization Strategies, it marks the locusNode as open and appliesthe process described in FIG. 180, FIG. 181, FIG. 182, FIG. 183, or FIG.184, respectively, for the various remaining Initialization Strategies.It should be clear to those skilled in the art of software developmentthat these processes could be merged, as long as each node isconstructed prior to its initialization.

As mentioned above in this section as “a convention that if a node ishidden, all of its descendants can be inferred to be hidden”, it may notbe necessary to descend through descendants to hide nodes if a node'sproperty of being hidden is inheritable. We make this assumption in FIG.179.

In some embodiments, an assumption about how to maintain the open/closedstatus of hidden nodes (those below a closed node) may be made.Embodiments may either initialize these to be closed and hidden andalso, upon collapsing a node, ensure that all its descendants that hadbeen shown are left in a closed and hidden state (so that upon opening anode we can assume that its children are closed) or else collapse thenon-leaf nodes where expansion stops. The figures assume the latter.They describe this step of collapsing nodes where expansion stopsseparately for each expansion strategy. Clearly, this could beabstracted, but that would require collecting those nodes whereexpansion stops so that they can be handled, well, collectively.

The Explicit Node Expansion Strategies use the template of FIG. 178.CurrentNode is initially the node being expanded. The process both marksthis node as open for expansion and, in sequence, hides any nodes forwhich the expansion strategy would create a conflict (defined broadly)by collapsing their parents and then applies that Explicit NodeExpansion Strategy to the node. For hiding nodes, Explicit NodeExpansion Strategy #1 and Explicit Node Expansion Strategy #2 use HideDirectly Conflicting Static Substructure 112111 from FIG. 185; ExplicitNode Expansion Strategy #3 and Explicit Node Expansion Strategy #4 useCollapse Siblings in Static Substructure 112100 from FIG. 186; andExplicit Node Expansion Strategy #5 may use either of these. Forexpansion, these strategies use Maximal Unfold Static Substructure111110, Unfold Static Substructure Until Common Descendants 110120,Unfold Static Substructure Until Multiple Nonleaf Children 110130,Unfold Static Substructure Until Multiple Children 110140, and UnaryUnfold Static Substructure 110150, from FIG. 180, FIG. 181, FIG. 182,FIG. 183, and FIG. 184, respectively.

The preceding describes Reopening Strategy #1. For Reopening Strategy#2, we mark nodes as they are opened, and then upon expansion if a nodehas not been so marked (and possibly if all its children are closed) actas above, otherwise show any open or empty descendants and the firstlayer of closed descendants. One can take this strategy further bystoring the tree structure at the end of a session and only initializingif no such stored structure is found.

FIG. 179 describes process Static Substructure Collapse 113100. Here,currentNode is initially the node being collapsed. In variousembodiments, the node must be marked for expansion and any visibledescendant nodes hidden. In various embodiments, nodes beneath a closednode will not be visible, so need not be hidden. But as long as a node'sproperty of being hidden is inheritable (the Static Lifetime Strategy),only the immediate children of the node being collapsed need be hidden.

We now describe the auxiliary operations related to each strategy. FIG.180 shows the process Maximal Unfold Static Substructure 111110. Itdescends through the substructure hierarchy, marking nodes as open andshowing each node, stopping (and marking nodes as closed) only toprevent showing any common descendants that have are already been madevisible through another path. FIG. 181 shows the process Unfold StaticSubstructure Until Common Descendants 110120. It is similar to MaximalUnfold Static Substructure 111110 but stops (and marks nodes as closed)to prevent showing any common descendants, whether or not they have arealready been made visible through another path. FIG. 182 shows theprocess Unfold Static Substructure Until Multiple Nonleaf Children110130. It also descends through the substructure hierarchy, markingnodes as open and showing each node, but stops (and marks nodes asclosed) at any node with multiple non-leaf children. FIG. 183 shows theprocess Unfold Static Substructure Until Multiple Children 110140. It issimilar to Unfold Static Substructure Until Multiple Nonleaf Children110130 but stops (and marks nodes as closed) to prevent descendingwhenever there are multiple children, whether or not any are leaves.Finally, FIG. 184 shows the process Unary Unfold Static Substructure110150. It takes exactly one step of unfolding.

These operations can be implemented for the Dynamic Lifetime Strategy byonly initially creating the locus node, and creating nodes where theyare made visible or destroying them where they are hidden in thedescription above. Further description should not be necessary since theother sections require dynamic substructure and context.

Presentation of DAG Context as an Inverted Tree

Here the tree grows upward and its purpose is to allow the user toexplore ancestors of a node, i.e., its context.

A DAG may have subtrees that extend upwards as well as downwards. Thefollowing two Locus Strategies relate to the notions of substructure vs.context.

-   -   Designated Locus Strategy: Some embodiments with a notion of a        locus node may consider ancestors of that node to be potential        context and descendants of that node to be potential        substructure. In degenerate cases, the entire DAG might be        considered either substructure or context. With this strategy,        only the designated locus node could be focused separately for        substructure or context (assuming both are available).        Substructure nodes could expand or collapse further substructure        and context nodes could expand or collapse further context.    -   Universal Locus Strategy: Other embodiments might consider        substructure and context to be relative terms. This could be        achieved by allowing any node to be focused separately for        structure or context. If a node within the closed substructure        frontier is collapsed for substructure, all of its proper        descendants are hidden; if a node on the closed substructure        frontier is expanded for substructure, some of its proper        descendants are exposed. If a node within the closed context        frontier is collapsed for context, all of its proper ancestors        are hidden; if a node on the closed context frontier is expanded        for context, some of its proper ancestors are exposed.

Two Parent Node Reordering Strategies are as follows:

-   -   Parent Node Reordering Strategy #1: Some embodiments may allow        multiple parent nodes to be expanded at the same time (as long        as no common ancestor is exposed at more than one node). The        order of the nodes is kept fixed.    -   Parent Node Reordering Strategy #2: Other embodiments may        restrict expansion such that the top node of a list of parent        nodes is expanded at least as far as any other node. If only one        context sibling is expanded at a time (per Explicit Node        Expansion Strategy #3, Explicit Node Expansion Strategy #4, or        Explicit Node Expansion Strategy #5), as any node is to be        expanded, it may be moved to the top. If multiple context        siblings may be expanded at the same time (per Explicit Node        Expansion Strategy #1 or Explicit Node Expansion Strategy #2),        for various embodiments the expansion process must be carried        out sufficiently to determine which context sibling requires the        most expansion and that context sibling may be moved to the top.        This may be for purposes of visualizing the relationships with a        common ancestor, as described below under “Presentation of        Common Context of Multiple Inverted Trees”.

The approach for the representation of a DAG as a tree, assuming theDesignated Locus Strategy and Parent Node Reordering Strategy #2 isshown for a particular DAG under navigation in FIG. 187. The root of theDAG (node 0) is at the bottom of this figure, while the root of the treeis at the top. The nodes listed above and to the left of any open nodeare collectively the parents of that node. Here, the nodes 0.0 through(n₀−1) are parents of node 0, and two of these (node 0.0 and node0.(n₀−2)) are open with their parents displayed.

Various embodiments that allow (per Parent Node Reordering Strategy #1)the top context sibling to be less expanded than any other contextsibling may manage indentation explicitly or manage invisible list nodes(since the uppermost node is not necessarily the leftmost); this can beavoided by reordering the context siblings (per Parent Node ReorderingStrategy #2). For one skilled in the art of software development,managing indentation or invisible list nodes involves only tedium, so weconcentrate on Parent Node Reordering Strategy #2.

Various embodiments implementing Parent Node Reordering Strategy #2 maybe constrained to also implement the Dynamic Lifetime Strategy becauseno static ordering may suffice. Embodiments for which there is aconvention that if a node is hidden then all of its descendants can beinferred to be hidden as well may also be constrained to also implementthe Dynamic Lifetime Strategy, because this convention is not compatiblewith an inverted tree where it should be possible to hide descendantswithout hiding the ancestors.

For embodiments implementing the Dynamic Lifetime Strategy, there is nodistinction between construction and initialization. FIG. 188 is similarto FIG. 177 except that it omits showing the locus node, as this isassumed to have been done during initialization of the substructure.Construction of the locus node, associated with the locus entity, isalso omitted as it is assumed to have been done during initialization ofdynamic substructure (not shown).

FIG. 189 shows the process of explicit expansion for situations where atmost one context sibling can be expanded at a time. It is similar toFIG. 178 but includes logic to handle two situations. It moves the nodebeing expanded to the top of the list of context siblings if it is notalready there. Also, if the node being expanded is at the bottom of thelist of context siblings and there is at least one other element of thelist, its descendants are transferred to the new last context sibling.For situations where multiple context siblings can be expanded at atime, it would have to first determine whether expanding this node wouldmake it the most expanded context sibling, and if so proceed with theabove logic to move it to the top of the list.

FIG. 190 shows the process Dynamic Context Collapse (Single Entity)213200. It repeatedly checks whether there is any more context abovecurrentNode, and if so deallocates currentNode's parent after movingcurrentNode with its descendants to currentNode's grandparent. Whenthere is no more context above currentNode, it is marked as closed forcontext expansion.

In the figures for the various strategies for unfolding context (FIG.191, FIG. 192, FIG. 193, FIG. 194, and FIG. 195) currentNode initiallyrefers to locusNode (for initialization) or for explicit expansion, tothe node being expanded. currentEntity refers to the entity associatedwith currentNode. Each of these dynamically allocate a list of nodes,one for each parent of currentEntity. To have these appear aligned butset back from currentNode, embodiments may place currentNode as a childof the last node in the list. Any time a strategy needs to recur toexpand on a newly created node, this allocation step may be repeated forthat node. The other main difference with the strategies for presentingsingle-entity DAG substructure is that it is sufficient to mark nodes asclosed for context expansion without any need to hide their contextdescendants, since nodes have not been created for those descendants.

FIG. 196 is similar to FIG. 185 but must search for conflicts in termsof entities and the DAG, and must take into account that to hide a nodethat is one of several parents in the DAG, various embodiments mustcollapse the node representing their DAG-child that is positioned as asubstrate-child of the node representing the last parent in thesequence. FIG. 197 is closely aligned with FIG. 186.

Presentation of Common Context of Multiple Inverted Trees

As described above under “Multiple Cross-kind Augmentation” as “byhaving multiple locus nodes”, it may be possible for a user to navigateto multiple locus nodes. Here a tree grows upward from each locus nodeas a user explores its ancestors, i.e., the node's context. Our aim isto identify, during context exploration, any paths from two or morelocus nodes that lead to a common ancestor.

We have had a methodology that as context is unfolded, we hide anycontext associated with an entity also associated with any context beingrevealed. Now that we have multiple locus nodes, if the same entitybecomes accessible via the context of more than one locus node, weproceed as follows. If that common ancestor entity would be revealedwith the same set of context siblings in each case, we merge the pathsto make this relationship apparent. If the common entity would berevealed with a set of context siblings, but was already showing with aproper subset of that set of context siblings, it would be incorrect tomerge the paths, as the entities associated with some of the newlyrevealed context siblings are not actually parents of the entityassociated with a node that would be presented as their collectivechild. Thus, we instead resolve the conflict by hiding the set ofcontext siblings that was previously being shown.

On the other hand, if the common entity would be revealed with a set ofcontext siblings, but was already showing with a proper superset of thatset of context siblings, we have at least two Children MergingStrategies:

-   -   Children Merging Strategy #1: One option is to proceed exactly        as in the proper subset case, with the implication that the set        of parents shown is always the exact and complete set of parents        of that entity.    -   Children Merging Strategy #2: Another option is to merge the        children of the proper superset of parents as context siblings        of the node being expanded, with the implication that the set of        parents shown need only be a subset of the parents of that        entity. This has the advantage that there is more “clumping” of        related nodes, but the disadvantage that some of a node's        parents are hidden.

Where embodiments are concerned with indicating common ancestors acrosslocus nodes, it may not be necessary to support continued exposure ofmore than one path at a time through the context of any locus node. Anembodiment might, however, expose paths from different locus nodesbetween which no common ancestor has yet been exposed and even expose“stubs” for any paths from a locus node other than those that lead to acommon ancestor with other locus nodes, possibly ensuring that these arepruned to be shorter than the path to the common ancestor. We are thusno longer concerned with Initialization Strategy #1, InitializationStrategy #2, Explicit Node Expansion Strategy #1, nor Explicit NodeExpansion Strategy #2.

Under “Presentation of DAG Context as an Inverted Tree”, we carefullyprevented the display of a common ancestor by distinct paths from thesame locus node (under the Designated Locus Strategy), or at all (underthe Universal Locus Strategy). This is effective in reducing excesscomplexity, and doing otherwise could defeat the benefits of thetree-based representation of the DAG. But in cases where we areinterested in several entities and have chosen to expand their context,one may be quite interested in seeing any common ancestor that isreached by those paths.

In expanding a context node, where only one parent can be expanded at atime, some embodiments may manipulate the order of the node's contextsiblings, so that the node being expanded is first in the list. Thatenables the context to grow outward in a natural tree structure. Otherembodiments may not rearrange their order, so that it is understood thatthe parents displayed relate to the node that is indented immediatelybeneath them, or that is in an open state.

We next show how shared context can be presented in a substrate tree, ormore abstractly as a forest, i.e. list of trees, of node lists, eachtree called a context frame. The forest can be presented in a substratetree by alternating indenting the node lists and their child contextframes. The approach is shown in FIG. 198 for a particular DAG undernavigation and Parent Node Reordering Strategy #2. We can see in thatdiagram the nested sequence of lists of two varieties. The outermostsubDAG list is a simple list whose elements are context frames. Contextframes contain a node list, in which each node provides informationregarding a different entity. Context frames may be internal or leaves.Leaves have a single node with an empty subDAG list and refer to a locusnode. Internal frames have a nonempty node list and a nonempty subDAGlist, with the intention that the listed nodes are collectively theparents of the uppermost open node in each subDAG. The subDAG list maybe positioned as a child of the last parent to take advantage ofsoftware that can visualize tree structure, or the sub-frames may beconsidered a single explicitly indented sibling of the parents, orindividual explicitly indented siblings of the parents, or theindentation can be globally managed explicitly by tracking the depth ofnesting of frames. For topmost internal frames, all nonorphan parentsare in the closed state. For other frames, only the first node is in theopen state and subsequent nodes are closed, indicating that parents atthe next level up have these first nodes as their collective children(while parents of the entities associated with closed nodes are notexposed). For convenience, we follow a convention for this diagram ofnumbering frames by appending a sequential number to the next outermostframe's number and numbering nodes by appending a sequential number tothe enclosing frame's number but one should keep in mind that theprocess of exploring context proceeds in an outward direction. We referto the number of parents listed for frame f as n_(f). Frame 0 and frame1 in FIG. 198 are two DAGs with no shared context. Frame 0 has parentnodes listed followed by three sub-frames representing subDAGs whoseroots (nodes 0.0.0, 0.1.0, and 0.2.0) are open and whose associatedentities all have the same set of parents (the entities associated withthose parent nodes). The successor parents in each frame (not endingwith “0.0”) are closed. This entire subDAG list may be positioned as achild of the last parent (node 0. (n₀−1)). It can be seen that thisstructure repeats recursively in the case of frames 0.0 and 0.1. Eachsuch recursion may reach one or more leaves. Frame 0.2 is a leaf, so ithas exactly one node (a locus node) listed and no sub-frames. This node,however, may carry the substructure associated with the correspondingentity. In the above description, lists are an abstraction that someembodiments may choose not to explicitly represent; such embodiments mayconsider a reference to a list above as simply referring collectively tothe elements of that list.

In FIG. 198, the closed context frontier for frame 0 consists of parent0.0 through parent 0. (n₀−1) plus all of the successor parents of anyembedded frames.

FIG. 199 through FIG. 202, present an example of how sharing of contextcould be experienced by a user of an embodiment. These screens displaythe process by which the user explores a DAG of skills. FIG. 199 showsan initial presentation of the DAG with three locus nodes, “Litigation”,“Legislating”, and “Networking”. Each is in a separate top-level frame.If from this position the user were to open the context for “Debate”, asuperskill of “Litigation”, we would see the result as in FIG. 200.“Debate” has two parents, “Communication” and “Analysis”. Since“Communication” without “Analysis” was a parent of “Networking”,“Networking” must for this embodiment be closed upon opening “Debate”,maintaining the invariant that any single skill appear only once. Now,opening “Interviewing” closes “Debate” and we see in FIG. 201 that,like, “Networking”, its sole parent is “Communication”, and these existin separate frames under “Communication”. Opening “Legislating” and then“Writing”, we see in FIG. 202 that it also falls under “Communication”as a third frame. Closing the folder for “Interviewing” might lead tothe screen in FIG. 203, with the frame including “Litigation” detachedand moved to the top level. The various frames are distinguished in thatthe uppermost folder in the parents for each frame is open while theremaining folders are empty or closed, but embodiments choose todistinguish them in other ways as well (for example, by drawing bordersaround them).

When collapsing context, we may now only want to remove context notshared with locus nodes outside of the node being collapsed (e.g., notshared with other frames). It is thus convenient to maintain withrespect to each frame or node references to the locus entitiesassociated with its descendant nodes. We do not show details ofmaintaining this information, as these should be clear to one skilled inthe art of software development.

In the first stage of the initialization process in FIG. 204, thestructure of FIG. 198 is set up with one top-level leaf frame per locusentity. The locus nodes are assumed to have been constructed duringDynamic Substructure Initialization for Multiple Entities. The remainderis similar to FIG. 188, but repeated for each locus node, and usingversions of the auxiliary routines particular to the need to shareacross multiple entities.

Dynamic context expansion for multiple entities is as presented in FIG.189, but the descendants referred to in “Move descendants of currentNodeto next to last context sibling” may be in the form of a list of frames.

FIG. 205 presents the process Dynamic Context Collapse (MultipleEntities) 223200, which begins similarly to the single-entity version inFIG. 190, but an additional step is required. If the frame listenclosing currentNode has more locus descendants than does currentNode,than we can't simply remove the context as this would drop locus nodes.(Note that by descendants here we do not mean literal descendants in thesubstrate tree, but rather context ancestors, related to descendants inthe underlying DAG. These correspond to currentNode along with thecontents of the framelist under currentNode's last sibling in thesubstrate.) Instead, we move currentNode to its own top-level frame, sothat those locus nodes are preserved, although they are not relevant tothe context of currentNode. Otherwise (removing the next layer ofcontext would not drop any locus nodes) we proceed as with FIG. 190.

The various strategies for unfolding dynamic context for multipleentities (Unfold Dynamic Context Until Multiple Nonleaf Children(Multiple Entities) 220230 in FIG. 206, Unfold Dynamic Context UntilMultiple Children (Multiple Entities) 220240 in FIG. 207, and UnaryUnfold Dynamic Context (Multiple Entities) 220250 in FIG. 208) contain asignificant amount of common logic implementing the methodology formultiple locus nodes of Children Merging Strategy #1, which is describedhere. Embodiments may begin by looking up the parents of currentEntityand determining whether they exist as a set of siblings in the substratetree (some embodiments may restrict this to nonempty sets ofparentNodes, since leaving multiple empty sets may not createconflicts). If so, they may simply move currentNode to a new frame underthat set of siblings. Otherwise, they may create that list of parentnodes, but also ensure that any existing overlapping set of contextsiblings is removed. The latter is described further in FIG. 210. Thisprocess of clearing the overlapping set of context siblings justdescribed might logically belong with Collapse Siblings in DynamicContext (Multiple Entities) 222200, but we place it here to be alongsideother checks for nodes associated with parents of currentEntity and sothat it may take place with each iteration. Another step indicated hereand described further in FIG. 211 is recommended, although someembodiments may omit it. As the expansion proceeds, nodes currently attop level but with the same parent set as that being unfolded (again,possibly excluding empty sets) may be captured by the newly expandednodes. It remains to construct the full list of nodes associated withthe parents of currentEntity. This is done such that currentNode (beingexpanded) is a child of the last such node.

FIG. 210 shows the logic for hiding conflicting visible nodes by raisingtheir DAG descendants to top level. Overlapping sets of context siblingscan be identified by locating nodes already associated with any of theseparent entities. Before removing the overlapping set, each frame underit (corresponding to one of their collective children in the DAG) ismoved to the top level list of frames. Recall that in any frame not attop level, the first context sibling is open (indicating that it isassociated with the child whose parents are being explored). Thus, thisfirst context sibling is closed as its frame is moved to top level.After each frame under a given subset of the context siblings has beenmoved, those nodes should be removed.

FIG. 211 shows the logic for capturing nodes associated with DAGsiblings of the entity whose node is being expanded. For each top-levelframe, if any of that frame's nodes has parents that are the same as theentities being revealed, then move that frame from the top level to be asibling of the node being expanded, move the matching node to the top ofthe frame, and open the context of that matching node.

At this point, the logic specific to each Explicit Node ExpansionStrategy comes into play, and is similar to what was described in FIG.193, FIG. 194, and FIG. 195. In fact, the first activity in each ofthose figures is the construction of the parent nodes, which we havejust described. The processes described here for multiple locus entitiesdiffer only in that the recursions for Unfold Dynamic Context UntilMultiple Nonleaf Children (Multiple Entities) 220230 and Unfold DynamicContext Until Multiple Children (Multiple Entities) 220240 continue withthe logic just described above as “Embodiments may begin . . . ”.

Presentation of Common Substructure of Multiple Trees

Here a tree grows downward from each locus node as a user explores itsdescendants, i.e., the node's substructure. Our aim is to identify,during substructure exploration, any paths from two or more locus nodesthat lead to a common descendant.

We have had a methodology that as substructure is unfolded, we hide anysubstructure associated with an entity also associated with anysubstructure being revealed. Now that we have multiple locus nodes, ifthe same entity becomes accessible via the substructure of more than onelocus node, we proceed as follows. If that common descendant entitywould be revealed with the same set of siblings in each case, we mergethe paths to make this relationship apparent. If the common entity wouldbe revealed with a set of siblings, but was already showing with adifferent but overlapping set of siblings, it would be incorrect tomerge the paths, as the entities associated with some of the newlyrevealed siblings are not actually children of the entity associatedwith a node that would be presented as their collective parent. Thus, weinstead resolve the conflict by hiding the set of siblings that waspreviously being shown.

On the other hand, if the common entity would be revealed with a set ofcontext siblings, but was already showing with a proper superset of thatset of context siblings, we have at least two options:

-   -   Parents Merging Strategy #1: One option is to proceed exactly as        in the proper subset case, with the implication that the set of        children shown is always the exact and complete set of children        of that entity.    -   Parents Merging Strategy #2: Another option is to merge the        parents of the proper superset of children as siblings of the        node being expanded, with the implication that the set of        children shown need only be a subset of the children of that        entity. This has the advantage that there is more “clumping” of        related nodes, but the disadvantage that some of a node's        children are hidden.

Where embodiments are concerned with indicating common descendantsacross locus nodes, it may not be necessary to support continuedexposure of more than one path at a time through the substructure of anysingle node. An embodiment might, however, expose paths from differentlocus nodes between which no common descendant has yet been exposed andeven expose “stubs” for any paths from a locus node other than thosethat lead to a common descendant with other locus nodes, possiblyensuring that these are pruned to be shorter than the path to the commondescendant. We are thus no longer concerned with Initialization Strategy#1, Initialization Strategy #2, Explicit Node Expansion Strategy #1, norExplicit Node Expansion Strategy #2.

Under “Presentation of DAG Substructure as a Tree”, we carefullyprevented the display of a common descendant by distinct paths from thesame locus node (under the Designated Locus Strategy), or at all (underthe Universal Locus Strategy). This is effective in reducing excesscomplexity, and doing otherwise could defeat the benefits of thetree-based representation of the DAG. But in cases where we areinterested in several entities and have chosen to expand theirsubstructure, one may be quite interested in seeing any commondescendant that is reached by those paths.

In expanding a substructure node, where only one child can be expandedat a time, some embodiments may manipulate the order of the node'ssiblings, so that the node being expanded is last in the list. Otherembodiments may not rearrange their order, so that it is understood thatthe children displayed relate to the sibling above them, with respect towhich they are indented.

We next show how shared substructure can be presented as a singlesubstrate tree. The approach is shown in FIG. 212 for a particular DAGunder navigation and Parent Node Reordering Strategy #2. We can see inthat diagram the nested sequence of lists of two varieties. Theoutermost root subDAG list is a simple list whose elements are rootsubstructure frames. Substructure frames have a main node followed byindented data (children in the substrate tree). Nodes may be open,closed, or empty (subject to comments above under “DETAILED DESCRIPTION”as “Some embodiments may choose to support only open and closed icons, .. . ”). We call a frame open, closed, or empty depending on the state ofits main node. The main nodes of elements of the outermost root subDAGlist have no shared substructure indicated. If the main node is open,the indented data includes a node list of closed children nodes followedby a substructure frame for the final child (any open child is assumedby some embodiments to be moved to the last position). Regardless of thestate of the main node, this data is followed by a root internal subDAGlist. Of course, this data may be organized as a single list or a listof lists as the embodiment finds convenient. root substructure framesare substructure frames in which the main node is a locus. Asubstructure frame is considered to be an internal substructure frame ora leaf substructure frame depending on whether or not there are anychildren nodes presented in the substrate tree, respectively (note thatthe represented entity need not be a leaf in the underlying DAG). Forvarious embodiments, the outermost root substructure frames may beleaves or internal, but other root substructure frames must be internal,as they lead to shared substructure. Define the full subDAG list as thelist formed by the final child substructure frame followed by theelements of the root internal subDAG list. Note that an opensubstructure frame may have an empty full subDAG list if the main nodehas no children in the substrate tree and the root internal subDAG listis empty. Define the height of a frame as follows. The height of a framewith an empty full subDAG list is one. Otherwise, the height of aninternal frame is one more than the height of the last frame in its fullsubDAG list. Define the terminal frame of an internal substructure frameto be the terminal frame of the last frame in its full subDAG list, ifany, or else the internal substructure frame itself. The frames in thefull subDAG list of an internal substructure frame will for someembodiments have increasing height. Define tail position as follows. Anytop level root subDAG list is in tail position. If a frame is in tailposition and has a non-empty full subDAG list, the last element of thefull subDAG list is in tail position. The terminal frame of a frame intail position is closed. The terminal frame of any other frame is open,and all such open frames may be aligned at the same depth in thesubstrate tree (root internal subDAGs are arranged so that this is thecase). It follows from the above that for various embodiments aninternal substructure frame in which the final child substructure frameis closed will have an empty root internal subDAG list. An internalframe in which the final child substructure frame is open may have anempty or nonempty root internal subDAG list.

The intention is that the nodes in the node list and the main node ofthe final child substructure frame are collectively the children of themain node of the enclosing substructure frame. (As always, children ofthe entities associated with closed nodes are not exposed). Moreover,the parents of a given descendant of the final root internal subDAG nodeinclude not only its immediate parent in the substrate tree, but alsoany open leaf nodes descended from any preceding elements of the fullsubDAG list and that are aligned with that immediate parent. The rootinternal subDAG list (or each of its elements) may be positioned as achild of the main node to take advantage of software that can visualizetree structure or the indentation can be globally managed explicitly bytracking the depth of nesting of frames. For convenience, we follow aconvention for FIG. 212 of numbering locus nodes sequentially, andotherwise numbering child nodes (including final child nodes that serveas the main node of a new frame) by appending a sequential number to thenumber of the next outermost frame's main node. Locus nodes 0 and 1 arethe main nodes of two top-level DAGs with no shared context, while node3.1.0 is a common descendant of locus nodes 0, 2, and 3. The parents inthe underlying DAG of the entity represented by node 3.1.0 include theentities represented by nodes 0.(n₀−1).(n_(0·(n) ₀ ⁻¹⁾−1), 2, and 3.1.In the above description, lists are an abstraction that some embodimentsmay choose not to explicitly represent; such embodiments may consider areference to a list above as simply referring collectively to theelements of that list.

The intention is that root substructure frames that are ancestors ofcommon descendants be placed so as to equalize the combined distancefrom the top level to the root substructure frame and from the rootsubstructure frame to the common descendant node. This can beaccomplished by storing a depth in the logical substructure tree witheach substructure node. Upon expanding a substructure node we check eachrevealed child for whether it already exists in the substrate. If itexists with depth greater than that of the node being expanded, collapsenodes as necessary and then move the top-level frame including theexpanded node downward by the difference in frames. If it exists with anequal or lesser depth than that of the node being expanded, then movethe children from the existing node to the node being expanded, andreorder the frames to maintain the invariant of increasing height.

It remains to explain how context can be presented along withsubstructure as a single substrate tree. A simple approach is that whena node is expanded for substructure, we first collapse any context ofthat node, so that we can start counting height with the locus nodes. Itshould be clear, however, that one could include context in the heightcalculation, and only collapse context when necessary to disassociatecommon ancestors.

Multiple Node Selection

This presentation framework can support selection of nodes, evenselection of a set of nodes, some of which conflict, in that they cannotall be displayed in the same tree. If the strategy for displaying nodesis restrictive, we shouldn't have to settle for only allowing the userto select nodes that can be visible together. Even if a node is nolonger visible, we can store its node or entity identifier or a pathfrom it to the root as a sequence of node or entity identifiers. Giventhe client's localized DAG structure, these should be sufficient for anypurpose. If the client needs to redisplay a selected node that is nolonger visible, it can do so using its path to the root, using Reveal ANode Accessible via a Path Through Substructure 112250 discussed aboveunder “Iterating DAG Augmentation” and diagramed in FIG. 213 or Reveal ANode Accessible via a Path Through Context 212250 discussed above under“DAG Generalization” and diagramed in FIG. 214. Rather than clearing theexisting tree and reopening by following the path, it is preferable tofollow the path from the root, tracking against any nodes that arealready displayed (we can assume that the root is always displayed),until reaching a node in the path that is not visible. Then, for eachnode on the path, close conflicting nodes (based on the strategy ineffect) and open (unfold) the next node on the path, selecting it fromthe set of children. An embodiment can choose to use any particularstrategy in unfolding nodes. If it unfolds only a single node at a time,it can assume that then subsequent nodes are not visible, and thus canunfold each after that point in quick succession.

An example of selecting a node and then performing an operation fromanother node after rearranging the substructure such that the selectednode is no longer visible is provided in figures FIG. 113 and FIG. 114,discussed above under “Generalization, Restatements, and Iteration”.

Auxiliary Information and Aggregations

Aggregations of Auxiliary Information

Various information can be associated with the entities related by theunderlying DAG. It is desirable to have an intuitive way of viewingrelevant auxiliary information while exploring the project hierarchy.Auxiliary information can be collected during the DAG reduction processand individual information regarding each entity stored in that entity'srecord in the localized DAG.

Examples of auxiliary information related to projects includetransaction data (contributions of funds or effort to a project, asdescribed below under “Contributions and Disbursements” as “Someembodiments may support contribution of funds . . . or effort . . . ”),total contributions, total funds available, progress reports forprojects, files uploaded, and streams of project activity. In the caseof files, the files themselves may not be provided to the client withthe local DAG, but only their metadata. The files could be downloaded oraccessed remotely as supported by the embodiment and directed by theuser. It may also include information about related entities, such asusers in various roles on a project (discussed above under “ProjectGovernance”) or skills required. Other auxiliary data such as tree sizeand recency of construction or access may not be displayed directly butrather utilized in providing “heat maps” of the interest in a particularnode as compared to its siblings. Embodiments may also support top-downspecification (by project administrators of parent projects) of astand-alone measure of the priority of a particular problem refinementor other project child. In the case of mutually exclusive projectrefinements, embodiments may support setting relative priorities amongthe various project refinements, perhaps using the techniques describedbelow under “Setting Percentages among Sibling Projects”.

Embodiments may allow auxiliary information associated with any oneentity to be viewed from any node referring to that entity, likely onlyat user request.

An “active” aggregation contains auxiliary information associated withcertain nodes under consideration by the user. Embodiments may considerthe active aggregation to consist of open and empty nodes, or preferablyof all visible nodes. To offer even more control, aggregations mayconsider only a user-selected subset of visible nodes to be in theactive aggregation, and these could be shaded appropriately or otherwisedistinguished. The active aggregation, though, should always consist ofa contiguous region including the locus node. Such an embodiment mightlet a user select an unselected node in the proper substructure orcontext for inclusion and that might implicitly include all nodes alongthe path to the locus. Conversely, it might let a user deselect aselected node in the proper substructure or context, and this wouldimplicitly deselect the logical tree rooted at that node. As nodes inthe hierarchy are expanded (or visible nodes selected), auxiliaryinformation associated with the newly revealed (selected) nodes might beadded to the active aggregation, while auxiliary information associatedwith nodes hidden during explicit collapse, as well as nodes hidden onimplicit collapse during expansion (or deselected), might be removedfrom the active aggregation. The active aggregation should be visiblealongside the primary DAG.

For each context node with a closed context expansion, there could be anaggregation over all its ancestors, including itself, or, preferably,over all of its proper ancestors, and for each closed substructure nodewith a closed substructure expansion, an aggregation over all itsdescendants, including itself, or, preferably, over all of its properdescendants (we refer to the former as “overall” and the latter as“constituent”). Rather than (or in addition to) presenting this for eachclosed expansion, some embodiments might present it only for the locusnode or nodes (in this case probably without regard to the state of DAGexploration, and probably including the locus nodes themselves). Theseaggregations are likely only presented at user request. Embodiments maywant to maintain the closed expansion aggregates for all nodes on theclosed frontier, or just calculate them when the aggregation isrequested. They may be cached so that they needn't be recalculatedfrequently during user interaction. If some of the entities representedby a closed folder have been deferred rather than passed to the client,as described under “Explicit DAG Augmentation by Specialization” as“When the user indicates a need to proceed deeper into the hierarchy . .. , additional nodes could be fetched by the server”, embodiments mayinclude a “More” link in the results, to inform the user that there maybe more auxiliary information and, if activated, to trigger loading ofadditional nodes and their auxiliary data into the local DAG.

Some embodiments might also want to support, alongside the activeaggregation, full overall and/or constituent aggregations, that mergethe information from all of the overall and constituent closed contextexpansions, respectively.

For example, a substructure node with a closed substructure expansionmay aggregate transaction data related to its proper descendants. Whenit is opened, the transaction data of each child may be made accessiblevia its node, and the substructure expansion of each child node(assuming that they are closed) may be associated with a separateaggregation of the transactions of its proper descendants.

We present another example as experienced by a user interacting with anembodiment in FIG. 215 through FIG. 226 for auxiliary informationconsisting of files. These files may be uploaded or downloaded by a userdragging their icons into or out of the appropriate region. Relevantfiles are displayed depending upon user interaction with the primary DAGin the “Dependencies” tab. We assume here that all visible nodes areincluded in the active aggregation. FIG. 215 shows a project screen withfive nodes visible. When a user hovers their cursor over the main iconof a visible node, the text “Aux” appears an if it is clicked on. Thus,we can see in FIG. 216 through FIG. 220 the files associated with eachindividual node and that the active aggregation includes all of thesefiles. FIG. 221 has an active aggregation including files associatedwith the locus node as well as the visible context; FIG. 222 includingfiles associated with the locus node as well as the visiblesubstructure; and FIG. 223 including files associated with locus nodeonly. The text “Aux” also appears when a user hovers their cursor over aclosed folder icon. FIG. 224 and FIG. 225 show that each of the closedfolders contains a project with a single file. Both of these can be seenfrom the constituent tab in FIG. 226.

Presenting Aggregate Auxiliary Information

For certain aggregations, in particular of scalar, quantitative valueswhere the aggregation takes less space than the included valuescollectively, including measures of the subtree size, embodiments maychoose to store the aggregates with every node, regardless of its state,and adjust these as necessary when the DAG is augmented.

For both active aggregations and “closed” aggregations, variousembodiments must take care to avoid double-counting the auxiliaryinformation of an ancestor or descendant that can be reached by morethan one path. For a union aggregation, double counting is not possibleand thus not a concern, but for other forms of aggregation it may wellbe.

When closing a folder, its aggregate may combine the individual valuesfor the disappearing descendant nodes (which must for variousembodiments be removed exactly once from the active aggregation) and theaggregates of their descendant expansions. If each piece of auxiliaryinformation in an aggregation is tagged with the residing entity of its“tree” node of origin (or equivalently, tagged with a DAG node), it ispossible to efficiently combine aggregations upon closing folderswithout double counting. Better yet, the auxiliary information can berepresented as a mapping to each datum, from the entity from which itoriginates. To combine aggregations upon closing folders, an embodimentcan begin with the individual data of the node being closed, maintaininga list of all entities represented. For each child node and each entitycontributing data to that child and not yet encountered, the embodimentcan merge that contributed data into the new aggregation.

To standardize this merging process, embodiments might separate key andvalue components of the information in an aggregate, reachable from someentity. The aggregate information might be maintained and presentedsorted by the key.

Upon a folder being opened, under various embodiments each child nodegets the previously closed folder's data that is associated with thenode itself, and that data is added to the active aggregation. Undervarious embodiments, each child node's expansion folder, if closed, getsaggregations that are subsets of the old aggregation for the node'spreviously closed expansion. Embodiments can check for each entity fromwhich the remaining data (not related to the entity of the node beingopened) originates, and for each child node, whether the entity is adescendant of the child node, and if so include its data in that child'saggregation. Alternatively, an embodiment might attempt to rebuild theaggregate for each child from its constituents.

To handle opening nodes more efficiently, data in the aggregations ofclosed nodes might take the form of a mapping, not from the residingentity of its node of origin, but from a representation of a “flow”,e.g., a DAG with distinguished source and sink, from the closed node tothe node of origin. These flows are not restricted to refinementrelations, but can include other relations as well.

The following representation for a DAG is suggested:

-   -   Flow|=flow(Source, Sink, FlowBody)    -   FlowBody|=link( )|sequence(Flow, Flow, Flow, . . . )|union(Flow,        Flow, Flow, . . . )

This grammar imposes that a flow has a distinguished source and sink,and a body that takes the form of a link, a sequence of two or moreflows, or a union of two or more flows. We additionally require herethat for sequences, the first flow has a source matching the sequenceflow's source, the last flow has a sink matching the sequence flow'ssink, and for each flow between the first and the last, the sourcematches the sink of the preceding flow and the sink matches the sourceof the subsequent flow; and that for a union, each flow in the union hassource and sink matching that of the union flow and that none of thevarious flows encompass each other.

We say that a sequence flow encompasses any sequence between the samesource and sink with the same number of segments, that substitutes forany component flows a flow that is encompassed by that segment flow. Wesay that a union flow encompasses any of the flows in its collection.The encompassing relation on flows is transitive and reflexive.

The intuition is that a flow is either empty (a link with source equalto sink), a simple arc between two nodes (a link, otherwise), a sequenceof flows that when connected end-to-end lead from the source to thesink, or a union of flows, all of which lead via alternate paths fromthe source to the sink.

These flows can be generated by scanning the DAG from a source node andeach time a particular node is encountered, adding the path by which itwas encountered to the existing flow as a union with a sequence of thelinks connecting elements along the path, unless the path was alreadyaccessible via the flow, in which case the flow can be left unchanged.

An alternative method of augmenting a flow with a path is as follows.For an empty flow, simply accept the path as a sequence of nonemptylinks. For a nonempty link, create a union with the sequence of nonemptylinks. For another sequence, if it has the same list of intermediateentities, create a sequence, augmenting each flow in the sequence withthe nonempty link Otherwise, create a union of the two sequences (it isalso possible to extract any common prefix and follow that by a union ofthe rest of each sequence). For a union, if the path is not encompassedby any elements of the collection, add it and remove any elements thatit encompasses. To augment a nonempty link with a nonempty link, simplyreturn the link. To augment a union with a nonempty link, if it is notalready in the union, add it.

Then, for various embodiments, when a closed node is opened, that nodegets as individual data the previously closed data that is associatedwith the empty flow from the node to itself (an empty union). Each ofits children can be assigned aggregate data associated with flowsobtained by deconstructing the previously closed node's flow into a setof pairs, each consisting of a node (corresponding to a child) and aflow from that node to the sink. Each child is assigned data for thoseflows for which it matches the node resulting from the deconstruction,under one of the flows resulting from the deconstruction.

The deconstruction process is as follows. For a link, the result is asingleton set of a pair of the sink node and the empty flow. For asequence, recur on the first flow in the sequence to obtain a set ofpairs; in each pair leave the node unchanged and modify the flow asfollows: if the original sequence was of length 2 and the pair's flow isempty, the flow in the pair is the second segment of the sequence.Otherwise, the flow is a sequence formed by substituting the pair's flowfor the first segment. For a union, recur on each element of the unionto obtain a set of pairs. For each entity represented as a node, form apair of that entity and the union of each flow in a pair with thatentity.

If information requests have been deferred by the sever, theaggregations for closed folders may not be complete, and can be enhancedby requesting additional data.

Embodiments may include or exclude inherited nodes in aggregatingauxiliary information, or they may give users a choice in the matter,perhaps via a checkbox. In the latter case, some embodiments maymaintain two versions of each aggregation (at least when inherited nodeswith auxiliary information are present), so that they can easily shiftbetween them, but other embodiments may recalculate aggregates upon theuser changing their selection. If inherited nodes are excluded, theirauxiliary information is not merged into any of the variousaggregations.

Particular Auxiliary Information

Setting Percentages Among Sibling Projects

In what follows, there is at various times a need to set percentages forallocating quantitative information regarding a parent project among itschildren. This can be done from the parent project itself, be enteringnumbers that total to 100, or, preferably, by adjusting the position oflines that divide a field into regions representing each child project(in some cases, it may be appropriate to select only children of aparticular kind (problem or solution)). It is even possible for thisdivision process to be superimposed on a tree-based view of a node'ssiblings.

Contributions and Disbursements

Some embodiments may support contribution of funds (perhaps only to aproblem) or effort (perhaps only to a solution) by users of the system.Such contributions could be triggered via options in the user's contextmenu when viewing such projects. Below we concentrate on funds, butembodiments may apply these concepts to effort as well, such as indisplaying summary contributions of effort to a solution.

The system may track funds that are contributed to a project, regardlessof whether or not those funds flow directly through to the projectadministrator. If not, various embodiments of the system will also wantto track disbursements for the purpose of the project, but if so, thismay or may not be desired.

It may be useful to support visualization of total funds contributed andtotal funds disbursed for projects in the context or substructure of alocus node. Embodiments might allow for this scalar data (describedabove under “Presenting Aggregate Auxiliary Information” as “inparticular of scalar, quantitative values . . . ”) to be displayed forindividual open nodes and aggregated for “overall” and “constituent”aggregations. Embodiments might further, in some situations, restrictthe DAG nodes displayed to those for which funds were contributed or forwhich funds were disbursed, or to those through which such nodes arereachable.

If funds are contributed to a project, a project administrator mightfind it desirable to use them for some lower-level project. This shouldalways be supported.

A project administrator might also find it desirable to use them forsome higher-level project. This could potentially be to makeinfrastructure or overhead expenditures that serve the entireorganization and thus take place at a higher level. Through the projectsettings, an allowable percentage can be set for upward transfers ofcontributions. Various checks can, if desired, be put in place toprevent or discourage funds transferred in an upward direction fromflowing downward to a sibling project. For example, a division can bemaintained between those funds eligible for downward transfer or not, oreven whether eligible for downward transfer to particular projects ornot (associating each partitioning of the total available funds with theset of eligible projects). More strictly, the system can registerexpectations of upward transfers (percentage or absolute) amongparticular child projects.

Cost information such as rents can be applied and tracked as time-basedauxiliary information at the level of the highest solution that relieson it. Alternatively, real estate can be viewed by embodiments as yetanother entity type, with its own hierarchical breakdown (by building,floor, etc.) and with a many-to-many cross-kind relation betweensolutions and locations.

Salary information is time-based, auxiliary information tied to theorganizational (user) hierarchy.

Both of these cases impose a need to allocate between the varioussolutions that an individual or location may be serving. This candefault to an even split, but be adjustable to any desired division. Inthe case of salary information, the division can be based ontime-tracking via check-ins (see below under “Project Check-ins” as“Check-ins . . . provide time-tracking information”).

Budgeting Support

Progress reports, mentioned above (under “Aggregations of AuxiliaryInformation” as “progress reports for projects”) provide qualitativeinformation regarding attainment of broad objectives that can be used byindividuals, whether at the heart of an organization or at itsperiphery, in judging its performance. Such measures also reflect on theindividuals responsible for those projects.

Embodiments might also support setting of quantitative goals as measuresof performance. Performance goals may be standardized (revenue,earnings, cost reductions, customer retention) or specific to a problem(perhaps improving standardized test scores of students within aschool). To support the latter, embodiments might support the definitionof performance measures with respect to a problem. In either case,time-based goals or forecasts may be established and tracked againstactual results. Embodiments may support various periodicities (annual,quarterly, monthly, etc.) and allow an initial value of goals orforecasts to be specified, perhaps along with selection of a functionfor increase or decrease over time. Indicators established for a problemare inherited through the project hierarchy (not just refinements) sothat lower-level projects can carve out responsibility for some degreeof the results, based on a percentage that is defined at the level ofthe parent project. Of course, lower-level projects can also establishtheir own performance measures. Establishment of a performance measureenables entry of corresponding results at the level of that project orlower-level projects. It is natural to display the various bases(goal/forecast/actual) against each other for a particular project.

In the case of embodiments that support mutually exclusive refinements(see above under “Mutually Exclusive Refinements” as “specializations ofa problem by distinct geographic areas could safely be consideredmutually exclusive”), it is possible to view performance for a singlemeasure against objectives as a multi-bar chart, with one bar per basis(goal/forecast/actual), normalized to be the same length or not, eachcoded by the contribution or expected contribution of each specializingproblem (or solution). Where there is a hierarchy (as in a standardmulti-level department and sub-department breakdown, or in a projecthierarchy including both problems and solutions), it is possible todrill down into the results. Perhaps by clicking on the portion of a barrepresenting a particular refinement, that bar might expand (replacingor alongside the previous bar) with its own multi-bar, reflecting thenext-lower down division of project structure.

Such sibling projects can be rated by the degree to which they meet orexceed expectations, highlighting projects at both ends of the scale.The order in which they are listed within each multi-bar in the barchart can reflect that ordering.

For any user, such charts can be viewed for each project in which theyare an administrator or collaborator. If the same performance measuresare in place across all of them, they can be merged, such that, asabove, one could drill down from the user level to each project.

General Data Sets

More generally, data sets may be associated with projects and aggregatedbased on user exploration of a localized DAG. Aggregated numeric datamay be presented in bar charts or graphs, with one bar or line,respectively, for each selected attribute (here and below, we considerboth directly stored and calculated data attributes). Geographic datacan be presented on a map, with discrete data points marked or eachregion shaded based on the level of aggregated values tied to it.

Individual projects can be associated with queries to a data set in theform of SQL, a URL, or any other form. The data for a particular node isthe result of resolving the query, e.g., of identifying relevantdatabase items (records, including those created by a logical joinoperation) and extracting appropriate attribute values from thoserecords. The specification of a data set will include, implicitly orexplicitly, the source of the database, conditions that must hold fordata items to be selected, and expressions of the attribute valuesextracted from those data items. A means of aggregating across theextracted data values of various selected data items may be included inthe latter expressions or provided separately. As the user expands anode, additional data points related to entities at newly exposed nodesare added to the visual presentation of the aggregation, and as the usercontracts a node, data points related to the entities at newly hiddennodes are removed, as described above.

To avoid having to open and close a database each time a node isaccessed, embodiments may allow the user to associate the database withthe least upper bound of entities from which queries to the database areto take place.

Project IP

A solution may be associated with a patent, a patent application, orwith particular claims of a patent or patent application.

Patents and claims may be treated by embodiments as entities. This wouldprovide an opportunity to tie the dependency structure of claims to thesolution refinement hierarchy. For example, an embodiment could supporta cross-kind relation from claims to solutions, as well as a refinementrelation over claims. Refining solutions could then inherit the claimsof the refined solution. Updating an inherited claim for a refiningsolution could create a diamond structure reflecting that the new claimboth describes the refining solution and refines the inherited claim.

Associating Code with Solutions

If a project is associated with a code repository under a traditionalversion control system, then a descendant solution may be associatedwith a (base) branch from that repository and any refining solution maybe associated with a derivative (perhaps indirectly so) branch. Asolution that refines multiple other solutions associated with branchesmay be associated with a branch that includes a merge of those branches.There is no guarantee that the code in the derivative branch will refinethe code in the base branch in any technical sense, and even if that isthe intention, it may hold only if the base branch is continuallyrebased into the derivative branch.

A solution may be associated with a (base) class in an object-orientedlanguage. Then, a refining solution may be associated with a classderived (perhaps indirectly) from that base class. Alternatively, asolution may be associated with a method of a (base) class. Then, arefining solution may be associated with the same method of a classderived (perhaps indirectly) from that base class. In either case, thereis no guarantee that the code in the derivative class will refine thecode in the base class in any technical sense. A solution that refinesmultiple other solutions associated with classes or their methods in alanguage supporting multiple inheritance may be associated with a classthat is derived from each of those classes, or a method of such a class.

DAG Filtering

It may be possible for a user to select via faceted browsing theentities to include in a DAG as loci by theircharacteristics/relationships/user history. This DAG filtering can bepresented to the user as a collection of checkboxes, one per possibleattribute value or kind of relationship, through which users indicatewhich entities to include based on whether they are set to any of thespecified values or are participating in any of the specifiedassociations with a distinguished entity such as the active user orlocus of the primary DAG. The user can then explore through other,related, entities and find relationships among the selected entities.Characteristics to filter by might include solution status (describedabove under “Associating a State Machine/Bayesian Network With Each Nodein a Refinement Hierarchy” as “solution status, with states for thevarious possible status values”). To filter by relationships, the usercould select one or more roles of theirs for which they would like tosee projects, as in FIG. 4. Alternatively, to filter by user historythey might select one or more actions (such as funding or volunteeringfor a project) as well as exactly one periodicity or a date range andview projects for which they performed those actions in that period. Forcontributions, it may also be possible to filter by the amountcontributed.

For a project administrator checked-in to a project (as described belowunder “Project Check-ins”), it may similarly be possible to select usersto include by selecting one or more roles, or time and contributiondescriptors.

A project administrator should also be able to select projects for whichmoney was contributed and those for which it was disbursed, for purposesof comparison, or projects for which effort was contributed.

It may be possible to further filter auxiliary information, for exampleby the periodicity (for example, annual, quarterly, monthly) or by thetime period, for historic as opposed to current information.

This DAG filtering can be implemented as follows. The server might builda local DAG including all possible entities, but marking some of them(and some of their ancestors and descendants) as hidden, based on eitherdefault selections or a record of the user's previous selections. If thevarious options are stored as separate database fields (for example asfields of distinct subclasses in an object-relational mapping (ORM)system), each of these may be accessed in creating lists of locusentities. The server might construct and pass to the client a mappingfrom facet values to the entity ids directly related to each such value,along with the set of entity descriptors, including sufficientinformation to determine, for each facet value selection, whether aparticular entity falls under that facet value selection. Importantly,with the hierarchical presentation of entities, a given entity is ofteninterpreted as falling under a facet value selection that corresponds toa relation with a distinguished entity if there is a direct associationbetween the distinguished entity and the given entity, or any properancestor of the given entity. Embodiments may take into account inconstructing such descriptors during DAG localization that if an entityfalls under a facet value, so do all of its descendants, and that if anentity does not fall under a facet value, neither do any of itsancestors. Such descriptors could include those constructed as describedbelow under “Project Check-ins” as “whether the user has rights undereach role for that project entity”. Under various embodiments, theclient should receive this map and the entity descriptors, andinitialize the context and substructure (or the server for the StaticLifetime Strategy) to show elements based on the initially selectedfacet values and descriptor information, and then handle eventsselecting or deselecting each facet value, keeping a record of whichfacet values are to be shown. Some embodiments may allow locus nodes tobe recognized as being related while others may not. When a facet valueis selected, the client shows all locus nodes that are directlyassociated with that value (via the mapping) and that are not alreadyshowing (or highlights them as locus nodes if they are already showingand the embodiment allows for this), and shows their context andsubstructure up to points where a node already showing is reached. Whena facet value is deselected, the client hides all locus nodes that aredirectly associated with that value (via the mapping) and for which theentity does not fall under another facet value still being shown (viathe entity descriptors). Merely de-highlight nodes where only the formeris satisfied. In either case, hide their context and substructure up topoints where a node's entity falls under a facet value still being shown(via the entity descriptors). The former process, Select a Facet Value021200 is in FIG. 227. The latter, Deselect a Facet Value 024200 is inFIG. 228.

A Method to Support Versioning and Conflict Resolution in ProjectHierarchies

Support for Distinct Project Views

Project Check-ins

Asking individual users to check into any one of their roles within aproject supports another form of context and provides the system withinsight into their intentions, enabling embodiments to customize bothoptions available to the user (perhaps through context menu options) andrecommendations (as under “Recommendations”) not only to the individualuser, but to a particular role on a particular project.

Embodiments might grant any user context menu options for publiclyavailable activities. Users with an association with a particularproject but who are not checked into that role could also be shown a“check into this role” option. A user could check into a role at theproject level at which they have their association or at any lowerlevel. Embodiments might allow users to check out of a project role fromsome global location, likely similar to how they would log out of thesystem. Embodiments may or may not restore a user's checked-in statuswhen they log out and back into the system. Some embodiments mightpresent users with options to check into another project role even whenthey are already checked into another such role, others might requirethe user to check out of one role before entering another. In the formercase, embodiments should implicitly check the user out of one role whenthey check into another. Some embodiments might allow the user to bechecked into multiple roles at once, in which case they would seecontext menu options for all relevant roles but then a particularactivity might be permissible under more than one role. Embodiments maynot allow a user to check into projects that are refinement descendantsof those to which they are directly involved if those refinementconnections involve traversing “weak” links, as described above under“Invitations and Applications to Connect” as ““weak” associationsbetween existing projects”.

Check-ins are also useful from a cost-tracking perspective, as theyprovide time-tracking information. Knowledge of the time spent by anindividual on various solutions (or projects more generally) can be usedin allocating their time between the various projects with which theyare involved.

FIG. 229 shows a user screen of the active user, with that user notchecked into any project. Because the user is administering the locusproject, he is able to see a context menu option to check into its childproject as an administrator, as shown in FIG. 230. Selecting this optionleads to the user being checked into that role, as shown in FIG. 231.Rather than just seeing the user's name in the pull-down menu at the topof the screen, we also see their current role and project. The optionsfor that menu now include “Checkout”. While checked in, on any screen towhich he navigates, this user may see context menu options andrecommendations related to their role on this project. After selecting“Checkout”, the user would revert to the state of FIG. 229.

This behavior can be supported by maintaining on the server a currentproject and current role for each user, which are empty when the user isnot checked into any project. The local DAG may be structured to includefor each project entity, whether the user has rights under each role forthat project entity (e.g., whether there is a direct participationassociation between the active user and that project or any of itsproper ancestor projects). This allows the client to determine where inthe hierarchy to show a check-in option. Embodiments may assume that ifa check-in option is available for any node, it is available for alldescendant project nodes. When creating new nodes, clients shouldmaintain a policy such as this, perhaps also assuming that the activeuser is an administrator of any new node or that if a new node has noancestors, the active user is an administrator, consistent with thepolicy of the server. Embodiments may or may not reload the client'spage when a change is made in the current project. Some embodiments maynot even require the server to know the checked-in status of any user.These embodiments would maintain locally the available menu options andrequest recommendations or time-tracking services based on the user'scheck-in activity.

Selective Knowledge Sharing

Moderation

Some embodiments arrange that contributions offered by the crowd areonly visible to the contributor and project administrator until they areapproved, and then may become visible publicly or become visible withinthe organization. When a change is submitted, it is marked as requiringapproval. Such systems may support at least a “global” view of a DAG,reflecting approved changes or changes not requiring approval, a userview, for each user, of the DAG reflecting changes awaiting approval bya moderator, and an “administrator” view, making available in some formall updates requiring approval. A user can view content reflecting bothaccepted changes and those by that user, whether or not submitted forapproval. It may be the case that all user changes are immediatelysubmitted for approval. Through the log of changes DAG, changes relatedto any user view and awaiting approval are visible to a projectadministrator. A facility may also be provided for a projectadministrator to assume a user view, to view content reflecting bothglobal changes and those submitted for approval by that user. Databaserecords (both change records and current records) should thus be markedas having been approved or not, with at least unapproved recordsincluding the id of the user who made the change so as to controlvisibility. The intention here is that once a record is approved, itbecomes “global”, but this designation can have any number of meaningsdepending on the access model supported by the embodiment and theorganization putting it to use; it may, however, potentially be visibleto people beyond the user making the change and those approving it.

Some embodiments may allow for the actions of administrators of aproject that is lower in the global DAG than another to require approvalby an administrator of that higher-level project. A sequence ofapprovals may thus be required in some cases.

The administrator, in reviewing changes, should be able to select among“accept” and “reject”, and if accepting should be able to select theaccess level (in a simple case, either publicly visible or private tothe organization).

To aid in moderation, a user acting (checked-in, as above under “ProjectCheck-ins”) as administrator of a project needs to be able to easilyidentify those entities requiring action, such as new projects requiringapproval.

Any user should be able to flag a public entity as requiring moderation.An embodiment might then, after one or more such reports and possiblydepending on other factors including the reputation of the flagginguser, the recency of the latest change, and the level of activity of theproject, roll back the last change to that entity for further review.

Project Access Setting

For simplicity we assume here “public” and “private” access levels, butof course more fine-grained settings are possible. Settings can bespecified by project role (below under “Project Governance” as“Individuals may associate with projects under various roles”),including for users unassociated with the project. Settings at theorganization or user level can determine the default visibility oftop-level projects. If a project is private, all lower-level projectsmay be assumed to be private. Thus, unless all parents of a project arepublic, embodiments may make it private. If all parents of a project arepublic, embodiments may default it to public, private, or requiremoderation, perhaps depending on the operation involved (e.g., refiningsolutions or problems, solving, componentizing, editing) or otherfactors.

Other Selective Knowledge Sharing

Embodiments might make use of project check-ins as described above under“Project Check-ins” so that users only have access related to aparticular project role when they are acting in that role.

As described above under “In-place, Iterating DAG Augmentation” as“restatements can also form a basis for controlling access”, thestructure of projects may be used to control what inherited project (orother entity) information is included in the response to a user request.

Hierarchical Version Control

Recording Independent Changes in Alternate Branches

If independent portions of the system change, those changes should berecorded as separate branches in a DAG. The advantage would be that anysingle independent change could be undone without disturbing presumablyunrelated changes. Such “disturbance” takes the form of conflicts, whichmust be resolved, putting a burden on the users involved. We do not haveperfect knowledge of what changes are independent, so the success ofthis approach is likely to depend on to what extent we can gain thisinsight.

For most purposes, different project settings can be considered to beindependent.

Text files are more difficult. It is possible to use “diff” filecomparison as with standard version control to identify modified lines.“diff” even groups changed lines into “hunks” that are assumed to berelated by their proximity, although this is a subjective process. Soeither every insertion, removal, or modification to a line could betreated as an independent change, or each “hunk” can be treated asindependent, for any definition of “hunk”.

Although “diff” generally works at the level of replacing entire lines,the same technology could be applied character by character, with “diff”files identifying which characters to replace. This would certainlyprovide more fine-grained identification of differences and thus moreseemingly independent changes. But it is not hard to come up withexamples where separate changes are intended to be performed as a unitand undoing one without the other could lead to unpredictable ordetrimental results. All of the changes submitted at the same time (partof the same editing “session”) might be considered a single change. Anoperation might also be provided to link two otherwise independentchanges so that they are to be considered a single change.

If changes are to be collected as entered, rather than when submitted,by restricting the editing options available to the user and recordingtheir actions, we can gain some insight into their intentions regardingthe changes and also avoid ambiguity such as that mentioned above under“DETAILED DESCRIPTION” as “there may be more than one way of recording achange to a file”. Where all changes are happening on a dedicatedplatform, this may be feasible. For example, an embodiment mightdisallow deletion other than of selected text, so that removal of ablock could be considered an atomic operation. This saves a system fromhaving to clump together those low-level operations that seem like theymight have been part of a higher-level operation.

If a later change subsumes multiple previous changes, those brancheswould merge. The larger, later change would have to be rolled backbefore any of the earlier smaller ones could be rolled back. Deletion ofthe entity would be an all-encompassing change in that it would subsumeall previous changes. So a DAG may take the form of an insertion nodeleading to various modification paths, all converging at a deletionnode.

If an entity is moved from one parent to another, for example a solutionis moved from one problem to another, in an embodiment in which suchcross-kind relations are many-to-one, that can be considered amodification to the solution. So we might have a path including“solution S created under problem P1”, followed by two branches:“solution S moved to problem P2” and “solution S text T1 replaced withtext T2 at char range . . . ”.

Because moving an entity is an atomic operation that is recorded by thesystem, we can treat it in this way.

Text being copied from one part of a text field to another wouldnaturally be considered an insertion, but by considering it specificallyas a copy, we could preserve that intention if it is reapplied after theoriginal text is modified.

If text is moved from one part of a text field to another, this couldalso be considered an atomic operation and doing so would preserve theintention if the move is reapplied after the original text is modified.The additional advantage for treating moved text as such is that we canplace the move on a single change branch, rather than treating it asseparate and independent deletions and insertions.

Each such atomic operation can be considered as a “commit” understandard version control. Traditionally in version control, every changeby default contributes to the next potential commit on the currentbranch. Work must be divided explicitly into sequential commits andparallel branches, and then explicitly merged.

For files that have been uploaded as auxiliary project data (above under“Aggregations of Auxiliary Information” as “Examples of auxiliaryinformation related to projects include . . . files uploaded”), there isa potential for integration with traditional version control.Embodiments that support online editing of uploaded files can have theserver register a commit after user submission or other recognition ofuser changes. In any case, a commit can be generated after each uploadof a file, including replacing files that have already been uploaded.Each such commit would correspond to a single modification change (witheach distinct file considered a separate sector). On a rollback, theserver could direct the traditional version control system to undodestroy that commit and reset to the previous commit.

Embodiments that support undoing a rollback (see below under “Historyand Conflicts” as “marking the change record as rolled back so that itsdisplay can indicate this and so that it can be available for having therollback undone”), would not destroy the commit but rather create a newbranch for it and store that rollback branch on the change record. Themaster branch would be set back to the previous commit. Upon undoing therollback, the master branch would be reset to point to the contents ofthe rollback branch and the rollback branch could be removed.

History and Conflicts

Divide possible changes among a fixed number of sectors. Sectors may bediscrete, as with configuration option selections, or they may berepresented as ranges or pairs or sets of ranges, for example of textchanged, removed, added, copied, or moved (see above under “RecordingIndependent Changes in Alternate Branches” as “Text being copied fromone part of a text field to another . . . ” and “If text is moved fromone part of a text field to another . . . ”) in a field. Edits todistinct text regions are potentially compatible with each other, as aredifferent children moved to a common parent (unless additional structureis required), or setting distinct configuration options. Edits to thesame sector potentially conflict, as do any other changes with recorddeletions. Standard practice of sequencing all modifications thencorresponds to treating each entity as a single sector.

Maintain change records for changes to any kind of user data on any kindof non-change record in the system. These changes are associated with aset of sectors and it is these change records that are arranged in aDAG. For various embodiments, the change record will generally containan indicator of any contents being dropped from the old record and anindicator of the new contents being installed. Each change recordaffects a set of sectors. The affected sectors can, for example, berepresented as a binary number with one bit per defined sector, althoughany number of representations are possible. It is possible to use fullhistory records rather than change records.

To form the global log DAG, treat each change record as an entity andconnect preceding records (as parents) with subsequent ones (aschildren) that affect any of the same sectors. This relationship ismany-many, but after each change, sectors are effectively partitionedsuch that for each partition there is a unique prior or subsequentchange record. As with other DAGs, the global log DAG can be localizedto a particular change, in this case to view predecessor states in thecontext and successor states in the substructure.

Some embodiments may treat distinct entities separately, even if theyare related. Others may go beyond the simple structure described aboveunder “Recording Independent Changes in Alternate Branches” as “a DAGmay take the form of an insertion node leading to various modificationpaths, all converging at a deletion node”. They may consider DAGaugmentations as changes to the augmenting records (specializations,generalizations, or cross-kind associations such as solutions), so thatit is not possible to roll back the creation of an entity withoutrolling back the creation of derivative entities. The change log of someentity originally created as a root node then includes all of itsaugmentations (direct and indirect) as well as modifications to theentity and any of those augmentations. This brings up an issue of how totreat moving an entity among various parents. Doing so could leave astub “move” node as a child of each source parent, and potentially asequence of “move” nodes with the moved child under the final target.

It should be possible to filter the log by user who made the change, orby project. Some embodiments may present the log as a secondary DAG (asdescribed above under “Secondary DAGs”) to responsible users orprojects, such that the log entries included vary with the range ofresponsible users. If logs are used to represent changes to otherentities, such as users or skills, then these can also be presented assecondary DAGS to either a user DAG for selecting a range of responsibleusers or the appropriate entity DAG, for selecting a range of entitieswhose changes should be included.

The selection of primary entities may likely affect how log entries aredisplayed. A deletion node (perhaps marked with “x”) may always be setas a leaf. A creation node (perhaps marked with “+”) may always be setas a root for an entity with no parents, but otherwise may be set, inthe logical tree, as a child of the creation node of any of its parents.A change node (perhaps marked with “˜”) may be set as a non-root node.If only viewing the dependent entity, the root of the log may be itscreation node and a move from one independent node to another under thesame cross-kind relation may be represented by an internal node (perhapsmarked with “>→”) associated with a sector dedicated to direct objectsunder that relation. Such nodes may be cascaded for multiple sequentialmoves. A move from one independent node to another under a differentcross-kind relation would be considered to affect the sectors forparents under both relations involved. Moves to or from parents underrefinement or other many-to-many relations may be treated as affecting aseparate sector for each parent entity involved. If viewing thedependent entity under an independent entity, its creation node may beset as an internal node affecting the sector for parents under thatcross-kind relation. The parent node could be the creation node for thatparent entity if the child entity were created directly as anaugmentation, or a move-from node (perhaps marked with “→”) if the childentity were moved to that parent. A move away from that parent (changeto its object), when viewing the dependent entity under its object, maybe represented as a leaf move-to node (perhaps marked with “>-”).Embodiments may choose to use other markings or icons.

A rollback operation can be initiated from any node of the DAG, and willfor various embodiments undo the entire subtree rooted at that node,beginning with the leaves (in any order) and working inward.

Similarly to links within the change hierarchy itself, a ‘latest’ changerecord (a leaf in the hierarchy) and the resulting current record areconnected by a database association. This may be necessary for extendingthe change hierarchy as users modify entity data. Again, sectors areeffectively partitioned such that for each partition there is a distinctlatest change record. The initial change record creating an entity isassumed to affect all sectors.

When a user or multiple users suggest changes to sectors that overlapwith those of a previous change, those changes are ordered; the priorchange is considered the “change of record” only for the set differencebetween the set of sectors affected by the prior change less the set ofsectors affected by the subsequent change, while the subsequent changeis considered the “change of record” for all of the sectors that itaffects.

As we have seen, branching occurs when a user or multiple users suggesta change to sectors that do not overlap with those affected by a priorchange. In that case, for various embodiments multiple child changerecords will be created under a single parent change record, related tonon-overlapping sectors.

Branching also occurs when distinct users (or the same user fromdifferent sessions) suggest different changes to follow the same priorchange, affecting overlapping sectors. This can happen when two users(or the same user in two sessions) check out a page before either ofthem updates the page. Such changes are considered to conflict.

Conflicts can also happen in systems that require moderators to approveuser changes before they become visible, as described above under“Moderation”. With such moderation, after any change (includingaugmentations, not just modifications) is submitted, the change ismarked as requiring approval. Only one current record may exist for anyentity key value and view (global or for a particular user). Databaserecords can be given an additional key of the user whose unapprovedchanges are reflected, or such content can be derived as necessary onpage loads from the global content by applying unapproved change recordsfor that user. In either case, change records for unapproved changesshould be identified by user and the latest such records may be madeaccessible for any user, entity, and sector selection.

Merging occurs when a user suggests a single change that affects thesectors of multiple prior changes, either directly (discussed aboveunder “Recording Independent Changes in Alternate Branches” as “If alater change subsumes multiple previous changes”) or when asserted as aresolution of conflicting prior changes. Conflict resolutions may or maynot themselves be considered to conflict with changes that affect any ofthe same sectors as affected by the changes being resolved (includingother resolutions of the same conflict).

For creation of a root entity, it is only necessary to create a user orglobal change record (depending on whether approval is required) withall sectors marked as affected and to associate this with a new user orglobal current record representing the entity.

When the server satisfies a load request for an existing entity for theclient, it can pass the client the mapping from sectors to changerecords. If the client then asks to mutate the entity, with that changerequest it can pass back to the server that mapping, or it can computethe previous change records for the affected sectors, and just passidentifiers for those records. Alternatively, the server can track whichclient sessions are working off of which change records. When the serverreceives from the client a request to make a particular change to aparticular record, it may need to create a change record for theaffected sectors along with any number of associations with the previouschange records for overlapping sectors, update the current record, andassociate it with the new change record.

Even after a change record is accepted and a current record updated (foreither approved or unapproved records), a subsequent request may bereceived that builds off of a prior change record. In such a case,embodiments may create a conflict post-facto and roll back theintervening changes so that the current record reflects the last commonstate of both sequences. In some situations, it may not be possible formore than a single change to have been made since the last common state.

Creation of a conflict record allows an administrator for a global viewor the user for a user view, to quickly identify and resolve theconflict. It contains references to the conflicting change records andthe sectors affected (in some unambiguous format such as in terms of thecommon ancestor state).

So first, if any approved change had been entered by any user or anyunapproved change had been entered by the same user (where approval isrequired) for an entity of the same key values, potentially conflictingsectors, and distinct changes, off of the same prior change record,neither has any clear precedence and only one current record may existfor that entity's key value and that view, so some embodiments may marksuch approved changes as unapproved and no longer current and create aconflict for an administrator to resolve, or mark such unapprovedchanges as no longer current and create a conflict for that user toresolve. Alternatively, it is possible to leave the change that hadsucceeded until the conflict is resolved.

The server can determine whether the change record upon which edits arebased is still current for the sectors affected. If no approval isrequired, it is only necessary to check whether the global record uponwhich the edits are based is still current. If not, there is a conflictwhich may be flagged. One approach is to consider the recent changes tobe unapproved changes belonging to the user who made them and restorethe global record by rolling them back until the global record uponwhich the edits are based is current. Then create a new unapprovedchange record, create a current record for the user reflecting thosechanges, and associate the new change record with the previous changerecord and the new current record. Another approach is to leave theglobal current record as is and create a new unapproved change recordand unapproved current record for this user view. If approval isrequired, the server should check both whether the user has any morerecent change records and whether the global record upon which anysequence of user edits was based is still current. If more recent userchange records are found, either of the options mentioned can be appliedfor the user, and the user can be left to resolve the conflict. If morerecent global records are found, it is not appropriate to roll anythingback. Again leave the global current record as is and create a newunapproved change record and unapproved current record for this userview. A process for handling change requests is in FIG. 232.

On viewing the log, an administrator should see a list of conflicts fordifferent sectors and be permitted to select one to resolve. Resolutionsshould allow selecting one of the updates or copying and pasting textbetween them, and then approving that change, or rejecting all changes.If the embodiment allows approval and rejection of changes to conflictwith other changes, a new resolution change is requested using RequestChange 001.

To approve a user change request for global view, the server shouldcheck for subsequent global changes that build off of a later changerecord for the affected sectors. If any exist, the unapproved changerecord should be made to follow those after assuring the conflict isappropriately resolved. Then, the change record can be marked asapproved and the current global record updated to reflect the changes.The current global record should be associated with this change record.If this was the final remaining unapproved change for that entity anduser view, there is no need for a current user record so it may bedeleted. Finally, if this approval is resolving a conflict, the conflictflag can be removed. A process for approving change requests is in FIG.233. We assume here that all preceding change records are approved. Tooperate with unapproved preceding change records, the process should beiterated over those, earliest first. Since change records form a DAG,embodiments may record visited records so as to process each only once.

Rejecting a change is slightly simpler. Delete the unapproved changerecord and then undo the changes it specifies in the user's currentrecord for that entity. The user current record should be associatedwith the prior change records. The remaining steps are similar to thoseof FIG. 233. A process for rejecting change requests is in FIG. 234. Weassume here that all preceding change records are approved. To operatewith unapproved preceding change records, the process should be iteratedover those, latest first. Since change records form a DAG, embodimentsmay record visited records so as to process each only once.

A user may also view the log to select a change record to be rolledback. Administrators select an approved change or a user's unapprovedchange to be rolled back, while general users select only their ownunapproved change to be rolled back. A change record not already rolledback may be selected to be rolled back. The operation of undoing changesspecified in a change record across alternative paths should becommutative, which should be possible since the changes on distinctpaths should be independent of each other. Users may, for example,restore records that have been deleted, so that they are available to beupdated by a current change based off of a prior state. This involvesmarking the change record as rolled back so that its display canindicate this and so that it can be available for having the rollbackundone. It also involves undoing the specified changes in the currentrecord and associating the current record with any change records priorto the one being rolled back. Again, we delete the user's current recordif it is no longer distinguished from the global one. A process forrolling back a single change record is in FIG. 235. We assume here thatany subsequent change records have already been rolled back and thatpreceding change records have not been rolled back. To operate withsubsequent change records not yet rolled back, the process should beiterated over those, latest first. Since change records form a DAG,embodiments may record visited records so as to process each only once.

If change approvals and rejections appear in the log with other changes,embodiments may support rolling them back, either explicitly or due tolater, conflicting approvals.

Preferred embodiments make rollbacks not necessarily permanent (a rogueor mistaken rollback could otherwise be very damaging). Rolled backchanges could be displayed as grayed out in the log. Thus rollbackscould themselves be undone. Undoing a roll-back would make it as if therollback never happened (so that there is no need to roll back an undoof a rollback).

A rollback could be done either by an administrator for global orindividual view or by an individual user only for individual view. Acurrent user record may need to be created if it did not already existand the rollback is being undone for a user. The change record should bemarked as not rolled back and made accessible from the current record,upon which the changes are replayed. A process for undoing rollbacks isshown in FIG. 236. We assume here that any previous change records arenot rolled back. To operate with rolled back previous change records,the process should be iterated over those, earliest first. Since changerecords form a DAG, embodiments may record visited records so as toprocess each only once.

Other Issues

Mutating DAGs

Because structures are rarely created perfectly the first time through,many embodiments may support operations to mutate the structure of aDAG. These operations could take place in the substructure or context,but some embodiments may restrict them to only the substructure.

Editing

Editing is the most straightforward form of DAG mutation, as it leavesthe structure in place. Just as individual nodes were modified duringin-place iteration, the same occurs during editing except that insteadof implicitly creating new nodes, the client and server really do modifythe information at a particular node.

Unlinking

Unlinking a node involves separating it from its parent in the logicaltree forming the substructure or the context. It may still be connectedby other links. If not, however, the node and all of its descendantsthat are not connected to other parts of the logical tree may bedestroyed, as they will for various embodiments become unreachable. Thiscan be implemented by descending through the tree, removing nodes withonly a single parent. Upon reaching a node with multiple parents, removethe link to the one from which it was reached and stop descending.

The client may perform this operation on the local DAG. The server mayneed to repeat it on the global DAG, and may find that nodes that wereunreachable in the local DAG are in fact reachable in the global DAG,and thus are not destroyed.

A locus node cannot be unlinked.

Deleting

There are actually two potential operations here, that can bedistinguished based on whether the node being deleted has a non-emptysubtree expanded, or whether it is either empty or closed.

If it is empty or closed, various embodiments may simply destroy thenode and all of its descendants (in the logical tree). As embodimentsdescend, they may remove any links to the nodes being deleted from othernodes. This operation can be performed on both the client and theserver, the only difference being that the server may remove additionallinks.

If the node's expansion folder is open, embodiments can destroy just theone node and replace in each of its children's list of parents, the nodebeing destroyed with the parent node from which it was accessed, andreplace in the list of children of the parent node from which it wasaccessed, the node being destroyed with each element of the list ofchildren of the node being destroyed.

Additional operations can be provided to delete a locus node, whichmight handle the various cases of its context and substructure foldersbeing open, closed, or empty as above.

The operation on open expansion folders is best suited for situationswhere there is only one relation between any two kinds of entities.Otherwise, the user may need to be queried for the relation that theywant to use in bridging the gap over the deleted node.

Cutting and Pasting

It is useful to be able to select a node, cutting it, and pasting itelsewhere. This can again take the form of multiple operations,depending on whether the expansion folder of the node being cut is openor closed/empty.

If the node being cut has a closed expansion folder, the intention is tomove the entire subtree elsewhere. The path to the locus from the nodebeing cut is captured and saved, and (as is standard practice) the imageof the cut node blurred slightly to indicate that it has been cut. Ifthere is no subsequent paste operation, (again as is standard practice)the cut node is restored unchanged. If there is a paste operation, thecut node is unlinked (just that node, which is not destroyed) and theparent by which it was accessed is replaced with the node to which it isbeing pasted.

If indirect objects are stored and the correspondence constraints under“Explicit DAG Augmentation by Specialization/Multiple simultaneousrefinement” or “DAG Generalization” are enforced, a proof is requiredthat is similar to the case of “DAG Refinement of Existing Entities”above when a refinement association is being created and the root nodebeing moved is a child in the local DAG of its object.

Cutting a node where its expansion folder is open can be interpreted assplicing out that node (similar to deletion of an open node above), andinserting it at the paste point as a child. Some embodiments might, ifthe expansion folder at the past point is open, splice in the singlenode below the past point node but above its children, but there is nosimilar splicing operation for an entire subtree.

The operation of cutting from an open expansion folder is again bestsuited for situations where there is only one relation between any twokinds of entities, for the same reason as for deletion above.

Refinement Text as Difference with Refined

Rather than merely using the text of a refined entity as the defaultinitial text for a specializing entity or the text of a refining entityas the default initial text for a generalizing entity, to be edited anddiscarded, embodiments may choose to store the difference in text alongwith the new text. Then, if part of the text that was not changed ismodified in the original entity, we can adjust the new entity'sdifference specification and recalculate its text so as to incorporatethe change to the original entity. For example, if in a specializationtext of 5 characters is added at a position 10 characters into thestring, and a later update to the refined node removes 3 characters (thefourth through sixth), the difference specification would be modified tosay that the text of 5 characters is added at a position 7 charactersinto the string and those three characters deleted from the refiningtext as well. This requires recording the specializing or generalizingentities of any existing entity or marking each refinement associationwith the direction in which it was applied, so that upon a modification,any specializing or generalizing entities (whether direct or via asequence of refinements) can be adjusted appropriately.

Project Governance

Individuals may associate with projects under various roles (potentiallyincluding administrator, advisor, collaborator, investor). Anadministrator is responsible for moderating project activity; andadvisor for providing feedback on ideas presented; a collaborator forhelping to implement projects (perhaps only solutions). An investor(funder) may or may not be treated as an advisor.

Various centralized and decentralized forms of project governance arepossible using these techniques, so it is an ideal framework with whichto compare their effectiveness. A centralized structure would have afixed set of administrators who would moderate all content. A lesscentralized structure would allow individuals associated with (or havingcreated) more general problems and solutions to make decisions on behalfof those projects, with those higher in the project hierarchy overrulingthose lower in the hierarchy. Augmentations to the project hierarchywould then be reviewed by those responsible for the entity or entitiesbeing augmented. Additionally, any or selected actions taken by the useraugmenting the project might be reviewable by administrators of theaugmented projects whenever such administrators deemed such oversightappropriate.

Alternatively, a voting mechanism could be established, likelyapportioning votes based on inferred influence within the project. Sincesome individuals may necessarily be more involved in the details ofprojects than others, but many individuals may know who they trust andrespect on a project, many embodiments may support governance byproxies, where people give to others authority to vote on their behalfto answer questions such as when solutions are to be implemented and howconflicts in modifying project structure are to be resolved. Such grantsof authority can be made for a particular project and be inheritedthrough the substructure of that project, but may be overridden for anyparticular elements of the substructure and their descendants. Variousembodiments may support chaining of proxy assignments.

Influence on a project can be inferred by subsequent activity related toproject structures created and/or edited by that individual, includingbut not exclusively augmentation of those project structures.

Engines, Components, and Logic

Certain embodiments are described herein as including logic or a numberof components, engines, or mechanisms. Engines may constitute eithersoftware engines (e.g., code embodied on a machine-readable medium) orhardware engines. A “hardware engine” is a tangible unit capable ofperforming certain operations and may be configured or arranged in acertain physical manner. In various example embodiments, one or morecomputer systems (e.g., a standalone computer system, a client computersystem, or a server computer system) or one or more hardware engines ofa computer system (e.g., a processor or a group of processors) may beconfigured by software (e.g., an application or application portion) asa hardware engine that operates to perform certain operations asdescribed herein.

In some embodiments, a hardware engine may be implemented mechanically,electronically, or any suitable combination thereof. For example, ahardware engine may include dedicated circuitry or logic that ispermanently configured to perform certain operations. For example, ahardware engine may be a special-purpose processor, such as aField-Programmable Gate Array (FPGA) or an Application SpecificIntegrated Circuit (ASIC). A hardware engine may also includeprogrammable logic or circuitry that is temporarily configured bysoftware to perform certain operations. For example, a hardware enginemay include software executed by a general-purpose processor or otherprogrammable processor. Once configured by such software, hardwareengines become specific machines (or specific components of a machine)uniquely tailored to perform the configured functions and are no longergeneral-purpose processors. It will be appreciated that the decision toimplement a hardware engine mechanically, in dedicated and permanentlyconfigured circuitry, or in temporarily configured circuitry (e.g.,configured by software) may be driven by cost and time considerations.

Accordingly, the phrase “hardware engine” should be understood toencompass a tangible entity, be that an entity that is physicallyconstructed, permanently configured (e.g., hardwired), or temporarilyconfigured (e.g., programmed) to operate in a certain manner or toperform certain operations described herein. As used herein,“hardware-implemented engine” refers to a hardware engine. Consideringembodiments in which hardware engines are temporarily configured (e.g.,programmed), each of the hardware engines need not be configured orinstantiated at any one instance in time. For example, where a hardwareengine comprises a general-purpose processor configured by software tobecome a special-purpose processor, the general-purpose processor may beconfigured as respectively different special-purpose processors (e.g.,comprising different hardware engines) at different times. Softwareaccordingly configures a particular processor or processors, forexample, to constitute a particular hardware engine at one instance oftime and to constitute a different hardware engine at a differentinstance of time.

Hardware engines can provide information to, and receive informationfrom, other hardware engines. Accordingly, the described hardwareengines may be regarded as being communicatively coupled. Where multiplehardware engines exist contemporaneously, communications may be achievedthrough signal transmission (e.g., over appropriate circuits and buses)between or among two or more of the hardware engines. In embodiments inwhich multiple hardware engines are configured or instantiated atdifferent times, communications between such hardware engines may beachieved, for example, through the storage and retrieval of informationin memory structures to which the multiple hardware engines have access.For example, one hardware engine may perform an operation and store theoutput of that operation in a memory device to which it iscommunicatively coupled. A further hardware engine may then, at a latertime, access the memory device to retrieve and process the storedoutput. Hardware engines may also initiate communications with input oroutput devices, and can operate on a resource (e.g., a collection ofinformation).

The various operations of example methods described herein may beperformed, at least partially, by one or more processors that aretemporarily configured (e.g., by software) or permanently configured toperform the relevant operations. Whether temporarily or permanentlyconfigured, such processors may constitute processor-implemented enginesthat operate to perform one or more operations or functions describedherein. As used herein, “processor-implemented engine” refers to ahardware engine implemented using one or more processors.

Similarly, the methods described herein may be at least partiallyprocessor-implemented, with a particular processor or processors beingan example of hardware. For example, at least some of the operations ofa method may be performed by one or more processors orprocessor-implemented engines. Moreover, the one or more processors mayalso operate to support performance of the relevant operations in a“cloud computing” environment or as a “software as a service” (SaaS).For example, at least some of the operations may be performed by a groupof computers (as examples of machines including processors), with theseoperations being accessible via a network (e.g., the Internet) and viaone or more appropriate interfaces (e.g., an Application ProgramInterface (API)).

The performance of certain of the operations may be distributed amongthe processors, not only residing within a single machine, but deployedacross a number of machines. In some example embodiments, the processorsor processor-implemented engines may be located in a single geographiclocation (e.g., within a home environment, an office environment, or aserver farm). In other example embodiments, the processors orprocessor-implemented engines may be distributed across a number ofgeographic locations.

Language

Throughout this specification, plural instances may implementcomponents, operations, or structures described as a single instance.Although individual operations of one or more methods are illustratedand described as separate operations, one or more of the individualoperations may be performed concurrently, and nothing requires that theoperations be performed in the order illustrated. Structures andfunctionality presented as separate components in example configurationsmay be implemented as a combined structure or component. Similarly,structures and functionality presented as a single component may beimplemented as separate components. These and other variations,modifications, additions, and improvements fall within the scope of thesubject matter herein.

Although an overview of the subject matter has been described withreference to specific example embodiments, various modifications andchanges may be made to these embodiments without departing from thebroader scope of embodiments of the present disclosure. Such embodimentsof the subject matter may be referred to herein, individually orcollectively, by the term “invention” merely for convenience and withoutintending to voluntarily limit the scope of this application to anysingle disclosure or concept if more than one is, in fact, disclosed.

The embodiments illustrated herein are described in sufficient detail toenable those skilled in the art to practice the teachings disclosed.Other embodiments may be used and derived therefrom, such thatstructural and logical substitutions and changes may be made withoutdeparting from the scope of this disclosure. The Detailed Description,therefore, is not to be taken in a limiting sense, and the scope ofvarious embodiments is defined only by the appended claims, along withthe full range of equivalents to which such claims are entitled.

It will be appreciated that an “engine,” “system,” “datastore,” and/or“database” may comprise software, hardware, firmware, and/or circuitry.In one example, one or more software programs comprising instructionscapable of being executable by a processor may perform one or more ofthe functions of the engines, datastores, databases, or systemsdescribed herein. In another example, circuitry may perform the same orsimilar functions. Alternative embodiments may comprise more, less, orfunctionally equivalent engines, systems, datastores, or databases, andstill be within the scope of present embodiments. For example, thefunctionality of the various systems, engines, datastores, and/ordatabases may be combined or divided differently.

The datastores described herein may be any suitable structure (e.g., anactive database, a relational database, a self-referential database, atable, a matrix, an array, a flat file, a documented-oriented storagesystem, a non-relational No-SQL system, and the like), and may becloud-based or otherwise.

As used herein, the term “or” may be construed in either an inclusive orexclusive sense. Moreover, plural instances may be provided forresources, operations, or structures described herein as a singleinstance. Additionally, boundaries between various resources,operations, engines, engines, and data stores are somewhat arbitrary,and particular operations are illustrated in a context of specificillustrative configurations. Other allocations of functionality areenvisioned and may fall within a scope of various embodiments of thepresent disclosure. In general, structures and functionality presentedas separate resources in the example configurations may be implementedas a combined structure or resource. Similarly, structures andfunctionality presented as a single resource may be implemented asseparate resources. These and other variations, modifications,additions, and improvements fall within a scope of embodiments of thepresent disclosure as represented by the appended claims. Thespecification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense.

Each of the processes, methods, and algorithms described in thepreceding sections may be embodied in, and fully or partially automatedby, code modules executed by one or more computer systems or computerprocessors comprising computer hardware. The processes and algorithmsmay be implemented partially or wholly in application-specificcircuitry.

The various features and processes described above may be usedindependently of one another, or may be combined in various ways. Allpossible combinations and sub-combinations are intended to fall withinthe scope of this disclosure. In addition, certain method or processblocks may be omitted in some implementations. The methods and processesdescribed herein are also not limited to any particular sequence, andthe blocks or states relating thereto can be performed in othersequences that are appropriate. For example, described blocks or statesmay be performed in an order other than that specifically disclosed, ormultiple blocks or states may be combined in a single block or state.The example blocks or states may be performed in serial, in parallel, orin some other manner. Blocks or states may be added to or removed fromthe disclosed example embodiments. The example systems and componentsdescribed herein may be configured differently than described. Forexample, elements may be added to, removed from, or rearranged comparedto the disclosed example embodiments.

Conditional language, such as, among others, “can,” “could,” “might,” or“may,” unless specifically stated otherwise, or otherwise understoodwithin the context as used, is generally intended to convey that certainembodiments include, while other embodiments do not include, certainfeatures, elements and/or steps. Thus, such conditional language is notgenerally intended to imply that features, elements and/or steps are inany way required for one or more embodiments or that one or moreembodiments necessarily include logic for deciding, with or without userinput or prompting, whether these features, elements and/or steps areincluded or are to be performed in any particular embodiment.

Any process descriptions, elements, or blocks in the flow diagramsdescribed herein and/or depicted in the attached figures should beunderstood as potentially representing modules, segments, or portions ofcode which include one or more executable instructions for implementingspecific logical functions or steps in the process. Alternateimplementations are included within the scope of the embodimentsdescribed herein in which elements or functions may be deleted, executedout of order from that shown or discussed, including substantiallyconcurrently or in reverse order, depending on the functionalityinvolved, as would be understood by those skilled in the art.

It should be emphasized that many variations and modifications may bemade to the above-described embodiments, the elements of which are to beunderstood as being among other acceptable examples. All suchmodifications and variations are intended to be included herein withinthe scope of this disclosure. The foregoing description details certainembodiments of the invention. It will be appreciated, however, that nomatter how detailed the foregoing appears in text, the invention can bepracticed in many ways. As is also stated above, it should be noted thatthe use of particular terminology when describing certain features oraspects of the invention should not be taken to imply that theterminology is being re-defined herein to be restricted to including anyspecific characteristics of the features or aspects of the inventionwith which that terminology is associated. The scope of the inventionshould therefore be construed in accordance with the appended claims andany equivalents thereof.

The invention claimed is:
 1. An apparatus comprising: aprocessor-implemented engine; memory coupled to theprocessor-implemented engine; and a display coupled to theprocessor-implemented engine, the apparatus implementing aspects of aproject management system, wherein the processor-implemented engine isdirected according to instructions stored in the memory, for each inputtree of one or more input trees, that input tree comprising a root nodeand for each other node a parent node of that other node, the one ormore input trees encompassed by a directed acyclic graph (DAG) in whichthat input tree is inverted such that that other node is a parent in theDAG of the parent node of that other node in that input tree, at leastone project node of that input tree indicating at least one project of aplurality of projects, to embed a respective displayed subtree of thatinput tree comprising the root node of that input tree and consisting ofa connected set of descendants of the root node of that input tree, therespective displayed subtree growing in a first direction, within asubstrate tree growing in a different direction than the firstdirection, each displayed node of each displayed subtree being indicatedby a respective substrate node of the substrate tree and each displayedchild of that displayed node being indicated by an ancestor in thesubstrate tree of the respective substrate node indicating thatdisplayed node, a respective extended displayed subtree of that inputtree subsuming the respective displayed subtree for each displayed nodein the respective displayed subtree of that input tree with children inthat input tree, the respective extended displayed subtree comprising arespective list of at least one parent node, the respective list of atleast one parent node containing one parent node for each parent in theDAG of that displayed node with children, by: a) receiving the one ormore input trees; b) for each input tree of the one or more input trees,presenting on the display via the substrate tree the respectivedisplayed subtree of that input tree; and c) upon direction by a user,expanding a given displayed node without children in the respectivedisplayed subtree of a given input tree of the one or more input treesand with children in the given input tree, the given displayed nodeindicating a given displayed project of the plurality of projects,embedding the respective extended displayed subtree for the givendisplayed node within the substrate tree, by: i) dynamically allocatingin the substrate tree a respective list of at least one parent substratenode for the given displayed node, each parent substrate node in therespective list of at least one parent substrate node indicating adisplayed child of the given displayed node in the respective extendeddisplayed subtree, the respective list of at least one parent substratenode comprising a first parent substrate node and a last parentsubstrate node; and ii) moving the respective substrate node indicatingthe given displayed node to descend in the substrate tree from the lastparent substrate node of the respective list of at least one parentsubstrate node for the given displayed node, thereby enabling the userto explore the plurality of projects through the respective displayedsubtree of the given input tree, growing in the first direction,embedded within the substrate tree, growing in the different directionthan the first direction.
 2. The apparatus of claim 1, wherein the givendisplayed node has a child displayed node in the DAG and the givendisplayed node is of greater height in the given input tree than anyother parent in the DAG of the child displayed node and the givendisplayed node is not already indicated by the first parent substratenode of the respective list of at least one parent substrate node forthe child displayed node, and the processor-implemented engine isfurther directed to: move the respective substrate node indicating thegiven displayed node to be sequenced as the first parent substrate nodeof the respective list of at least one parent substrate node for thechild displayed node, thereby maintaining expansion of the first parentsubstrate node of each list of at least one parent substrate node atleast as far as any other parent substrate node of that list of at leastone parent substrate node.
 3. The apparatus of claim 2, wherein thegiven displayed node was initially indicated by the last parentsubstrate node of the respective list of at least one parent substratenode for the child displayed node and the processor-implemented engineis further directed to: move a plurality of descendant nodes that aredescended in the substrate tree from the respective substrate nodeinitially indicating the given displayed node to descend in thesubstrate tree from the parent substrate node now sequenced as the lastparent substrate node of the respective list of at least one parentsubstrate node for the child displayed node, thereby maintaining eachsubstrate node indicating a respective child node that is related as achild to the parent node of the given displayed node in the given inputtree within a context exploration of the respective substrate nodeindicating the parent node of the given displayed node in the giveninput tree.
 4. The apparatus of claim 2, a plurality of the root node ofeach input tree of the one or more input trees sharing a common ancestorin the DAG, wherein: a) the substrate tree comprises a plurality oflists of at least one substrate node, each list of at least onesubstrate node of the plurality of lists of at least one substrate nodecomprising a last substrate node, and a plurality of context frameforests, an inner list of at least one substrate node of the pluralityof lists of at least one substrate node being nested within a contextframe tree of an outer context frame forest of the plurality of contextframe forests in the substrate tree and an inner context frame forest ofthe plurality of context frame forests comprising at least one contextframe tree being nested within an outer list of at least one substratenode of the plurality of lists of at least one substrate node in thesubstrate tree, wherein: i) a respective list of at least one substratenode of the plurality of lists of at least one substrate node isdescended in the substrate tree from each context frame tree of eachcontext frame forest of the substrate tree; and ii) the inner contextframe forest is descended in the substrate tree from the last substratenode in the outer list of at least one substrate node; b) the outer listof at least one substrate node comprises the substrate node indicatingeach parent in the DAG of the displayed node indicated by the firstsubstrate node of the list of at least one substrate node nested withineach context frame tree in the inner context frame forest, the outerlist of at least one substrate node being the respective list of atleast one parent substrate node for the first substrate node of the listof at least one substrate node nested within the first context frametree in the inner context frame forest; and c) each context frame forestof the plurality of context frame forests represents a DAG contextexploration from each first substrate node of the list of at least onesubstrate node of each context frame tree of that context frame forest,an outermost context frame forest representing the DAG contextexploration in a suspended state and the inner context frame forestrepresenting the DAG context exploration in an active state, therebydisplaying a single representation of the DAG context exploration fromthe common ancestor in the DAG of the plurality of the root node of eachinput tree of the one or more input trees.
 5. An apparatus comprising: aprocessor-implemented engine; memory coupled to theprocessor-implemented engine; and a display coupled to theprocessor-implemented engine, the apparatus implementing aspects of aproject management system, wherein the processor-implemented engine isdirected according to instructions stored in the memory to: a) receive alocalized DAG comprising a plurality of local entities and a pluralityof local associations, the plurality of local entities subsuming aplurality of local projects, the plurality of local projects comprisingat least one locus project, each local association of the plurality oflocal associations relating a child entity and a parent entity of theplurality of local entities, each local entity of the plurality of localentities being ascended or descended in the localized DAG from arespective at least one source locus project of the at least one locusproject for that local entity; b) visually present each locus project ofthe at least one locus project on the display, that locus projectindicated by: i) a context root node of a respective context treegrowing in a first direction from that locus project, a respectivecontext subtree rooted at each node of the respective context tree, therespective context tree being the respective context subtree for thecontext root node; or ii) a substructure root node of a respectivesubstructure tree growing in a different direction than the firstdirection from that locus project, a respective substructure subtreerooted at each node of the respective substructure tree, the respectivesubstructure tree being the respective substructure subtree for thesubstructure root node, the context root node and the substructure rootnode coinciding and indicating the locus project where both the contextroot node and the substructure root node are presented for a locusproject of the at least one locus project; and c) upon direction by auser, collapse and expand: i) the respective context subtree for a givencontext node indicating a given context project of the plurality oflocal projects, within the respective context tree for a given contextsource locus project of the respective at least one source locus projectfor the given context project, wherein upon expansion of the givencontext node, prior to presenting a plurality of presented given contextproject ancestor entities that are ascended in the localized DAG fromthe given context project, the plurality of presented given contextproject ancestor entities comprising at least one already-visible propercontext entity, each already-visible proper context entity of the atleast one already-visible proper context entity indicated by arespective already-visible proper context node on the respective contexttree for the given context source locus project, the respectivealready-visible proper context node already visible on the display as achild of a respective already-visible parent context node, the apparatusselectively collapses the respective already-visible parent context nodefor each already-visible proper context entity of the at least onealready-visible proper context entity; or ii) the respectivesubstructure subtree for a given substructure node indicating a givensubstructure project of the plurality of local projects, within therespective substructure tree for a given substructure source locusproject of the respective at least one source locus project for thegiven substructure project, wherein upon expansion of the givensubstructure node, prior to presenting a plurality of presented givensubstructure project descendant entities that are descended in thelocalized DAG from the given substructure project, the plurality ofpresented given substructure project descendant entities comprising atleast one already-visible proper substructure entity, eachalready-visible proper substructure entity of the at least onealready-visible proper substructure entity indicated by a respectivealready-visible proper substructure node on the respective substructuretree for the given substructure source locus project, the respectivealready-visible proper substructure node already visible on the displayas a child of a respective already-visible parent substructure node, theapparatus selectively collapses the respective already-visible parentsubstructure node for each already-visible proper substructure entity ofthe at least one already-visible proper substructure entity, therebyenabling the user to explore the plurality of local entities as beingascended or descended in the localized DAG from each locus project ofthe at least one locus project, via the respective context tree for thatlocus project or the respective substructure tree for that locusproject, respectively, with each entity of the plurality of localentities indicated by at most one visible node.
 6. The apparatus ofclaim 5, wherein the processor-implemented engine is further directedto: a) where the at least one locus project comprises a second givencontext source locus project distinct from the given context sourcelocus project, upon expansion of the given context node: i) for a firstpresented given context project ancestor entity of the plurality ofpresented given context project ancestor entities, each parent entitythat is related as a parent in the localized DAG to the first presentedgiven context project ancestor entity being indicated by a firstrespective already-visible child proper context node that is a child ofa common already-visible parent context node on the respective contexttree for the second given context source locus project, arrange thefirst presented given context project ancestor entity on the display toshare the first respective already-visible child proper context nodeindicating each parent entity with the common already-visible parentcontext node as context; and ii) for a second presented given contextproject ancestor entity of the plurality of presented given contextproject ancestor entities, prior to presenting a plurality ofparents-to-be-displayed within the plurality of presented given contextproject ancestor entities on the display, a respective association ofthe localized DAG relating each parent-to-be-displayed of the pluralityof parents-to-be-displayed as parent of the second presented givencontext project ancestor entity, each already-visible parent entity ofat least one already-visible parent entity of the plurality ofparents-to-be-displayed indicated by a second respective already-visiblechild proper context node that is a child of an already-visible parentcontext node on the respective context tree for the second given contextsource locus project, and each not-yet-visible parent entity of at leastone not-yet-visible parent entity of the plurality ofparents-to-be-displayed not indicated by any already-visible node on thedisplay, selectively collapse the already-visible parent context node onthe display; or b) where the at least one locus project comprises asecond given substructure source locus project distinct from the givensubstructure source locus project, upon expansion of the givensubstructure node, i) for a first presented given substructure projectdescendant entity of the plurality of presented given substructureproject descendant entities, each child entity that is related as achild in the localized DAG to the first presented given substructureproject descendant entity being indicated by a first respectivealready-visible child proper substructure node that is a child of acommon already-visible parent substructure node on the respectivesubstructure tree for the second given substructure source locusproject, arrange the first presented given substructure projectdescendant entity on the display to share the first respectivealready-visible child proper substructure node indicating each childentity with the common already-visible parent substructure node assubstructure; and ii) for a second presented given substructure projectdescendant entity of the plurality of presented given substructureproject descendant entities, prior to presenting a plurality ofchildren-to-be-displayed within the plurality of presented givensubstructure project descendant entities on the display, a respectiveassociation of the localized DAG relating each child-to-be-displayed ofthe plurality of children-to-be-displayed as child of the secondpresented given substructure project descendant entity, eachalready-visible child entity of at least one already-visible childentity of the plurality of children-to-be-displayed indicated by asecond respective already-visible child proper substructure node that isa child of an already-visible parent substructure node on the respectivesubstructure tree for the second given substructure source locusproject, and each of at least one not-yet-visible child entity of theplurality of children-to-be-displayed not indicated by anyalready-visible node on the display, selectively collapse thealready-visible parent substructure node on the display, therebypresenting to the user a common context exploration from the respectivecontext tree for the given context source locus project and therespective context tree for the second given context source locusproject or a common substructure exploration from the respectivesubstructure tree for the given substructure source locus project andthe respective substructure tree for the second given substructuresource locus project, with each set of local entities within theplurality of local entities represented on the display by at most onevisible set of children nodes.
 7. The apparatus of claim 5, eachcontributing local project of a plurality of contributing local projectswithin the plurality of local projects being associated with orderedauxiliary project information, the ordered auxiliary project informationcomprising a plurality of items maintained to be accessed in order assorted by a key, wherein the processor-implemented engine is furtherdirected to: a) dynamically aggregate the ordered auxiliary projectinformation via a merging process across a plurality of visible localprojects currently visible to the user within the plurality of localprojects, generating a dynamically-changing aggregation comprising anaggregated plurality of items within the plurality of items; and b)present the dynamically-changing aggregation to the user, therebyenabling the user, while exploring the plurality of local projects,being a customized collection of projects, as ascended or descended inthe localized DAG from the at least one locus project, to visualize thedynamically-changing aggregation of the ordered auxiliary projectinformation across the plurality of visible local projects, the orderedauxiliary project information associated with a now-hidden project ofthe plurality of contributing local projects being removed from thedynamically-changing aggregation upon removal of a node indicating thenow-hidden project from the display, a particular item of the aggregatedplurality of items being of the auxiliary project information associatedwith a common ancestor project of the plurality of contributing localprojects, the common ancestor project ascended in the localized DAG froma first locus project of the at least one locus project and from asecond locus project of a second at least one locus project of theplurality of local projects, the particular item appearing in a seconddynamically-changing aggregation alongside a neighboring item of theplurality of items but not of the aggregated plurality of items.
 8. Theapparatus of claim 7, the apparatus implementing aspects of a socialnetwork, the apparatus comprising networking hardware supporting theprocessor-implemented engine in acting as a client communicating withone or more computing devices, wherein the processor-implemented engineis further directed to request and receive the localized DAG from aserver, the localized DAG extracted by the server from a global DAG, theplurality of associations comprising: a) a social refinement associationindicating that the child entity for the social refinement associationrefines the parent entity for the social refinement association, thechild entity and the parent entity for the social refinement associationbeing of the plurality of contributing local projects and of theplurality of visible local projects, the child entity for the socialrefinement association being created by a first user and beingassociated with a first organization and the parent entity for thesocial refinement association being created by a second user and beingassociated with a second organization, the social refinement associationbeing a mutually approved, directed connection; and b) a non-socialassociation, the child entity and the parent entity for the non-socialassociation being of the plurality of contributing local projects and ofthe plurality of visible local projects and being created by the seconduser and being associated with the second organization, the non-socialassociation not requiring mutual approval, thereby causing thedynamically-changing aggregation to include ordered auxiliary projectinformation for the child entity and the parent entity for both thesocial refinement association and the non-social association.
 9. Anapparatus comprising: a processor-implemented engine; memory coupled tothe processor-implemented engine; and networking hardware supporting theprocessor-implemented engine in acting as a server communicating withone or more computing devices, wherein the processor-implemented engineis directed according to instructions stored in the memory to: a)receive identification of at least one locus project of a plurality ofprojects from a client; b) extract a respective localized directedacyclic graph (DAG) localized to the at least one locus project, therespective localized DAG of a plurality of localized DAGs, from a globalDAG comprising a plurality of entities and a plurality of associations,the plurality of entities subsuming the plurality of projects, eachassociation of the plurality of associations relating a child entity anda parent entity of the plurality of entities; c) perform areconfiguration upon the respective localized DAG; and d) transfer therespective localized DAG to the client, the respective localized DAGcomprising: 1) a plurality of local entities comprising a constituententity corresponding to each entity of a plurality of particularreachable entities within the plurality of entities, each entity of theplurality of particular reachable entities being ascended or descendedin the global DAG from a respective at least one source locus project ofthe at least one locus project of the plurality of projects by arespective at least one path, at least one constituent locus projectcorresponding to the at least one locus project; and 2) a plurality oflocal associations comprising a constituent association corresponding toeach association of the plurality of associations on the respective atleast one path for each entity of the plurality of particular reachableentities, that constituent association relating the constituent entitycorresponding to the child entity for that association as a child localentity and the constituent entity corresponding to the parent entity forthat association as a parent local entity, wherein: i) the plurality ofassociations subsumes a plurality of refinement associations, eachrefinement association of the plurality of refinement associationsindicating that the child entity for that refinement association refinesthe parent entity for that refinement association, the reconfigurationcomprising, for each inheritable entity of a respective at least oneinheritable entity of the plurality of entities for the at least onelocus project, that inheritable entity descended in the global DAG froma respective inheritable child entity by a respective inheritable entitypath, the plurality of projects comprising a respective properrefinement ancestor project that is related as a parent in the globalDAG to the respective inheritable child entity and that is ascended inthe global DAG from a respective inheriting locus project of the atleast one locus project by a respective inheritance path by way of arespective sequence of one or more refinement associations of theplurality of refinement associations, a deep inheritable component ofthe respective at least one inheritable entity not being the respectiveinheritable child entity, a respective constituent inheriting locusproject of the at least one constituent locus project corresponding tothe respective inheriting locus project: A) where that inheritableentity is a non-locus-descended inheritable entity not descended in theglobal DAG from any locus project of the at least one locus project: I)the plurality of local entities comprising a respective inherited entitycorresponding to the non-locus-descended inheritable entity; and II) theplurality of local associations comprising a respective inheritingassociation with the respective inherited entity corresponding to thenon-locus-descended inheritable entity as the child local entity andwith the respective constituent inheriting locus project for thatinheritable entity being ascended in the respective localized DAG forthe at least one locus project from the parent local entity; and B)where that inheritable entity is a locus-descended inheritablecomponent, an already-inherited-or-constituent component correspondingto the locus-descended inheritable component being descended in therespective localized DAG for the at least one locus project from therespective constituent inheriting locus project for that inheritableentity: I) the plurality of local associations comprising a respectivemerging association with the already-inherited-or-constituent componentas the child local entity and with a parent inherited entitycorresponding to the parent of the locus-descended inheritable componentalong the respective inheritable entity path as the parent local entity,thereby supporting the client in enabling a user of the client torequest the respective localized DAG for the at least one locus projectand then visualize as descended from the respective constituentinheriting locus project and initiate an operation upon the respectiveinherited entity corresponding to the deep inheritable component withinan integrated hierarchy with parents comprising at least one inheritedparent entity corresponding to an inheritable parent entity on therespective inheritable entity path for the deep inheritable componentand at least one other parent entity not corresponding to anyinheritable parent entity on the respective inheritable entity path forthe deep inheritable component.
 10. The apparatus of claim 9, theapparatus implementing aspects of a social network, the respectiveinheritance path for an automatically-shared inheritable entity of therespective at least one inheritable entity comprising: a) a socialrefinement association, the child entity for the social refinementassociation being created by a first user of the client and beingassociated with a first organization and the parent entity for thesocial refinement association being created by a second user of theclient and being associated with a second organization, the socialrefinement association being a mutually approved, directed connection;and b) a non-social refinement association, the child entity and theparent entity for the non-social refinement association being created bythe second user and being associated with the second organization, thenon-social refinement association not requiring mutual approval, therebyinheriting the automatically-shared inheritable entity as the respectiveinherited entity corresponding to the automatically-shared inheritableentity through the social refinement association and through thenon-social refinement association.
 11. The apparatus of claim 9,wherein: a) the plurality of projects subsumes a plurality of problemsand a plurality of solutions, no project being in both the plurality ofproblems and the plurality of solutions; b) the plurality of refinementassociations comprises: i) a problem refinement association that relatesa child problem of the plurality of problems and a parent problem of theplurality of problems, indicating that the child problem specializes theparent problem; or ii) a solution refinement association that relates achild solution of the plurality of solutions and a parent solution ofthe plurality of solutions, indicating that the child solutionelaborates upon the parent solution; and c) the respective at least oneinheritable entity comprises an inheritable project of the plurality ofprojects, wherein: i) the inheritable project is an inheritable solutionof the plurality of solutions, the respective inherited entitycorresponding to the inheritable solution being an inherited solution ofthe plurality of local entities, the respective inheriting locus projectfor the inheritable solution being a respective inheriting locus problemof the plurality of problems and the respective proper refinementancestor project for the inheritable solution being a respective properrefinement ancestor problem of the plurality of problems; or ii) theinheritable project is an inheritable problem of the plurality ofproblems, the respective inherited entity corresponding to theinheritable problem being an inherited problem of the plurality of localentities, the respective inheriting locus project for the inheritableproblem being a respective inheriting locus solution of the plurality ofsolutions and the respective proper refinement ancestor project for theinheritable problem being a respective proper refinement ancestorsolution of the plurality of solutions, thereby supporting the clientenabling the user to visualize as descended in the respective localizedDAG for the at least one locus project from the respective constituentinheriting locus project and initiate the operation upon the inheritedsolution corresponding to the inheritable solution, the inheritablesolution addressing the respective proper refinement ancestor problem, amore general problem than the respective inheriting locus problem, orthe inherited problem corresponding to the inheritable problem, theinheritable problem decomposing the respective proper refinementancestor solution, a less elaborate solution than the respectiveinheriting locus solution.
 12. The apparatus of claim 11, the at leastone locus project being at least one locus problem of the plurality ofproblems, the plurality of entities subsuming a plurality of conditioncomponents, the respective at least one inheritable entity being arespective at least one inheritable condition component of the pluralityof condition components, wherein: a) at least one data-based contextproblem of the plurality of problems is the respective proper refinementancestor project for each inheritable condition component of therespective at least one inheritable condition component, the at leastone data-based context problem being implicitly or explicitly associatedwith a respective database of a plurality of databases, the respectivedatabase for each data-based context problem comprising data arranged asa plurality of attributes, at least one data-based inheriting locusproblem being the respective inheriting locus project for eachinheritable condition component of the respective at least oneinheritable condition component; b) the plurality of conditioncomponents subsumes a plurality of terms that express equalities orinequalities over at least one attribute for at least one database ofthe plurality of databases and comprises at least one Boolean operator;c) each attribute referenced by a term of each condition component ofthe plurality of condition components is for a database associated witha data-based context problem ascended in the global DAG from thatcondition component; and d) the processor-implemented engine is furtherdirected to: i) formulate a query relating to the at least one locusproblem, the query comprising a condition comprising the respective atleast one inheritable condition component, the query supportingaggregation of results; ii) resolve the query on the respective databaseof each condition component of the query to obtain a query result; andiii) transfer the query result to the client, thereby integrating thestructure of the respective at least one inherited entity correspondingto the respective at least one inheritable condition component with thestructure of at least one already-inherited-or-constituent conditioncomponent descended in the respective localized DAG for the at least onelocus problem from the at least one constituent inheriting locus projectfor the respective at least one inheritable condition component, the atleast one inherited condition component and the at least onealready-inherited-or-constituent condition component being of theplurality of condition components, supporting the client in motivatingand tracking progress in addressing the at least one locus problem bypresenting the query result, serving as a measure by which the at leastone locus problem is quantified, the query formulated from therespective at least one inheritable condition component for the at leastone locus problem, gathered as relevant to the at least one data-basedinheriting locus problem.
 13. The apparatus of claim 12, wherein: arefining data-based problem of the at least one data-based inheritinglocus problem refines each refined data-based problem of at least onerefined data-based problem of the at least one data-based contextproblem, each refined data-based problem of the at least one refineddata-based problem having a respective at least one condition componentdescendant in the global DAG, and the condition for the refiningdata-based problem being formulated as a conjunctive condition, being aconjunction of a respective condition formulated for each refineddata-based problem of the at least one refined data-based problem fromthe respective at least one condition component descendant for thatrefined data-based problem, thereby supporting the client in enablingthe user to implicitly associate the conjunctive condition with therefining data-based problem upon navigating to the refining data-basedproblem.
 14. The apparatus of claim 12, wherein: a refined data-basedproblem of the at least one data-based inheriting locus problem isrefined by each refining data-based problem of at least one refiningdata-based problem of the plurality of problems, each refiningdata-based problem of the at least one refining data-based problemhaving a respective at least one condition component descendant in theglobal DAG, and the condition for the refined data-based problem beingformulated as a disjunctive condition, being a disjunction of arespective condition formulated for each refining data-based problem ofthe at least one refining data-based problem from the respective atleast one condition component descendant for that refining data-basedproblem, thereby supporting the client in enabling the user toimplicitly associate the disjunctive condition with the refineddata-based problem upon navigation to the refined data-based problem.15. The apparatus of claim 12, the query result comprising a pluralityof data items, wherein: the server labels at least one labeled localrefinement association of the constituent association corresponding toeach refinement association of the plurality of refinement associationswith at least one constraint that the child project of that refinementassociation requires, beyond any constraint required by the parentproject of that refinement association, thereby supporting the client inincrementally presenting a dynamically-changing aggregation of dataitems across a customized collection of projects determined by the user.16. The apparatus of claim 11, the plurality of entities subsuming aplurality of state machine components, the respective at least oneinheritable entity being a respective at least one inheritable statemachine component of the plurality of state machine components, wherein:a) at least one state-based context project of the plurality of projectsis the respective proper refinement ancestor project for eachinheritable state machine component of the respective at least oneinheritable state machine component, at least one state-based inheritinglocus project being the respective inheriting locus project for eachinheritable state machine component of the respective at least oneinheritable state machine component; b) the plurality of state machinecomponents subsumes a plurality of state machine states; and c) theprocessor-implemented engine is further directed to: i) formulate astate machine relating to the at least one locus project, the statemachine comprising the respective at least one inheritable state machinecomponent; and ii) transfer a form of the state machine to the client,thereby associating a hierarchical state machine, layered over therespective localized DAG for the at least one locus project as ahierarchy of problems and solutions, formulated from the respective atleast one inheritable state machine component for the at least one locusproject, gathered as relevant to the at least one state-based inheritinglocus project, and integrating the structure of the respective at leastone inherited entity corresponding to the respective at least oneinheritable state machine component with the structure of at least onealready-inherited-or-constituent state machine component descended inthe respective localized DAG for the at least one locus project from theat least one constituent inheriting locus project for the respective atleast one inheritable state machine component, the at least oneinherited state machine component and the at least onealready-inherited-or-constituent state machine component being of theplurality of state machine components.
 17. The apparatus of claim 16,wherein the processor-implemented engine is further directed to: a)gather a plurality of records, each record comprising at least oneattribute value of the respective proper refinement ancestor project foran inheritable state machine component of the respective at least oneinheritable state machine component, along with a plurality of orderedpairs of states, each inheritable state of an ordered pair ofinheritable states of the plurality of ordered pairs of states being ofthe respective at least one inheritable state machine component, eachordered pair of states of the plurality of ordered pairs of statesindicating a respective transition from the first state of that orderedpair to the second state of that ordered pair, for a project describedby the at least one attribute value of that record; and b) formulate thestate machine from the plurality of ordered pairs of states for eachrecord of the plurality of records as training data, thereby enabling adistinct state machine to be derived from the plurality of records as acustomized combination of training data relevant to the at least onelocus project, the training data comprising the respective transitionfor the ordered pair of inheritable states.
 18. The apparatus of claim9, wherein: upon direction from the client based on a modification bythe user to an original inherited entity, the original inherited entitybeing the respective inherited entity corresponding to a giveninheritable entity of the respective at least one inheritable entity forthe at least one locus project, yielding a modified inherited entity,the original inherited entity corresponding to the given inheritableentity being descended in the respective localized DAG for the at leastone locus project from the respective constituent inheriting locusproject for the given inheritable entity by the respective inheritingassociation, the server relates the given inheritable entity to therespective inheriting locus project for the given inheritable entity bycreating in the global DAG, yielding a resulting global DAG: a) arestating entity, wherein the restating entity is created as an entityin the plurality of entities and the modified inherited entitycorresponds to the restating entity; b) a first association with therestating entity as the child entity and with the respective inheritinglocus project for the given inheritable entity as the parent entity,wherein the first association is created as an association in theplurality of associations; and c) a second association with therestating entity as the child entity and with the given inheritableentity as the parent entity, wherein the second association is createdas a refinement association in the plurality of refinement associations,thereby creating the restating entity to restate the given inheritableentity with respect to the respective inheriting locus project for thegiven inheritable entity, supporting the client in implementing anin-place modification of the original inherited entity to the modifiedinherited entity.
 19. The apparatus of claim 18, wherein the serverreceives identification of a second at least one locus project of theplurality of projects from a second client and transfers to the secondclient the respective localized DAG for the second at least one locusproject, the at least one locus project being a first at least one locusproject, the second at least one locus project comprising anotherrefinement descendant in the global DAG of the respective properrefinement ancestor project for the given inheritable entity, the otherrefinement descendant not being ascended or descended in the global DAGfrom the respective inheriting locus project for the given inheritableentity, wherein: the restating entity is not among the respective atleast one inheritable entity for the second at least one locus project,thereby supporting the client in avoiding distracting the usernavigating to the second at least one locus project with the restatingentity, restating with respect to the respective inheriting locusproject for the given inheritable entity, unrelated to the otherrefinement descendant.
 20. The apparatus of claim 18, wherein the serverreceives identification of a second at least one locus project of theplurality of projects from a second client and transfers to the secondclient the respective localized DAG for the second at least one locusproject, the at least one locus project being a first at least one locusproject, a refinement descendant locus project of the second at leastone locus project being descended in the global DAG from the respectiveinheriting locus project of the first at least one locus project for thegiven inheritable entity, a first inheriting locus project, by acontinued inheritance path from the refinement descendant locus projectby way of a continued sequence of one or more refinement associations ofthe plurality of refinement associations, wherein: the given inheritableentity is not among the respective at least one inheritable entity forthe second at least one locus project, thereby supporting the client inavoiding distracting the user navigating to the second at least onelocus project with the given inheritable entity, related to therespective proper refinement ancestor project for the given inheritableentity by the respective inheritable entity path to the respectiveinheritable child entity, the restating entity being among therespective at least one inheritable entity for the second at least onelocus project and refining the given inheritable entity, the restatingentity being related by the first association to the first inheritinglocus project, descended in the global DAG from the respective properrefinement ancestor project by the respective inheritance path.
 21. Anapparatus comprising: a processor-implemented engine, memory coupled tothe processor-implemented engine; and networking hardware supporting theprocessor-implemented engine in acting as a client communicating withone or more computing devices, wherein the processor-implemented engineis directed according to instructions stored in the memory to requestand receive a localized directed acyclic graph (DAG) from a server, thelocalized DAG extracted by the server from a global DAG, the global DAGcomprising a plurality of entities and a plurality of associations, theplurality of entities subsuming a plurality of projects, eachassociation of the plurality of associations relating a child entity anda parent entity of the plurality of entities, wherein the localized DAGcomprises: 1) a plurality of local entities comprising a constituententity corresponding to each entity of a plurality of particularreachable entities within the plurality of entities, each entity of theplurality of particular reachable entities being ascended or descendedin the global DAG from a respective at least one source locus project ofat least one locus project of the plurality of projects by a respectiveat least one path, at least one constituent locus project correspondingto the at least one locus project, a respective at least one sourceconstituent locus project of the at least one constituent locus projectcorresponding to the respective at least one source locus project; and2) a plurality of local associations comprising a constituentassociation corresponding to each association of the plurality ofassociations on the respective at least one path for each entity of theplurality of particular reachable entities, that constituent associationrelating the constituent entity corresponding to the child entity forthat association as a child local entity and the constituent entitycorresponding to the parent entity for that association as a parentlocal entity, the localized DAG having been reconfigured by the server,presenting to a user who navigates to the at least one locus project amanner of exploring through related entities, wherein: a) the pluralityof associations subsumes a plurality of refinement associations, eachrefinement association of the plurality of refinement associationsindicating that the child entity of that refinement association refinesthe parent entity of that refinement association; and b) the user isenabled to visualize as descended in the localized DAG from a respectiveconstituent inheriting locus project of the at least one constituentlocus project a respective inherited entity of the plurality of localentities corresponding to each inheritable entity of at least oneinheritable entity of the plurality of entities, each inheritable entityof the at least one inheritable entity descended in the global DAG froma respective inheritable child entity by a respective inheritable entitypath, the plurality of projects comprising a respective properrefinement ancestor project that is related as a parent in the globalDAG to the respective inheritable child entity and that is ascended inthe global DAG from a respective inheriting locus project of the atleast one locus project by a respective inheritance path by way of arespective sequence of one or more refinement associations of theplurality of refinement associations, the respective inheriting locusproject corresponding to the respective constituent inheriting locusproject, a deep inheritable component of the at least one inheritableentity not being the respective inheritable child entity, the localizedDAG having been reconfigured such that for each inheritable entity ofthe at least one inheritable entity: A) where that inheritable entity isa non-locus-descended inheritable entity not descended in the global DAGfrom any locus project of the at least one locus project: I) theplurality of local entities comprising the respective inherited entitycorresponding to the non-locus-descended inheritable entity; and II) theplurality of local associations comprising a respective inheritingassociation with the respective inherited entity corresponding to thenon-locus-descended inheritable entity as the child local entity andwith the respective constituent inheriting locus project for thatinheritable entity being ascended in the localized DAG from the parentlocal entity; and B) where that inheritable entity is a locus-descendedinheritable component, an already-inherited-or-constituent componentcorresponding to the locus-descended inheritable component beingdescended in the localized DAG from the respective constituentinheriting locus project for that inheritable entity: I) the pluralityof local associations comprising a respective merging association withthe already-inherited-or-constituent component as the child local entityand with a parent inherited entity corresponding to the parent of thelocus-descended inheritable component along the respective inheritableentity path as the parent local entity, thereby enabling the user tovisualize as descended from the respective constituent inheriting locusproject and to initiate an operation upon the respective inheritedentity corresponding to the deep inheritable component within anintegrated hierarchy with parents comprising at least one inheritedparent entity corresponding to an inheritable parent entity on therespective inheritable entity path for the deep inheritable componentand at least one other parent entity not corresponding to anyinheritable parent entity on the respective inheritable entity path forthe deep inheritable component.
 22. The apparatus of claim 21, eachcontributing project of a plurality of contributing projects within theplurality of projects being associated with ordered auxiliary projectinformation, the ordered auxiliary project information comprising aplurality of items maintained to be accessed in order as sorted by akey, the local entity corresponding to each contributing project beingassociated with the ordered auxiliary project information alsoassociated with that contributing project, wherein: theprocessor-implemented engine is further directed to generate via amerging process and present to the user an aggregation of the orderedauxiliary project information comprising an aggregated plurality ofitems: a) across a plurality of substructure projects within theplurality of local entities, each substructure project of the pluralityof substructure projects being descended in the localized DAG from therespective at least one source constituent locus project for thatsubstructure project and corresponding to a global substructure projectof the plurality of projects; or b) across both the plurality ofsubstructure projects and a plurality of context projects within theplurality of local entities, each context project of the plurality ofcontext projects being ascended in the localized DAG from the respectiveat least one source constituent locus project for that context projectand corresponding to a global context project of the plurality ofprojects, the plurality of substructure projects comprising therespective inherited entity corresponding to an inheritable contributingproject of the at least one inheritable entity and of the plurality ofcontributing projects, thereby enabling the user to visualize theaggregation of the ordered auxiliary project information across theplurality of substructure projects or the aggregation of the orderedauxiliary project information across both the plurality of substructureprojects and the plurality of context projects, the plurality ofsubstructure projects comprising the respective inherited entitycorresponding to the inheritable contributing project within theintegrated hierarchy, a first item of the aggregated plurality of itemsbeing of the ordered auxiliary project information associated with afirst inheritable contributing ancestor of the inheritable contributingproject through the respective proper refinement ancestor project forthe first inheritable contributing ancestor and a second item of theaggregated plurality of items being of the ordered auxiliary projectinformation associated with a second inheritable contributing ancestorof the inheritable contributing project through the respective properrefinement ancestor project for the second inheritable contributingancestor.
 23. The apparatus of claim 21, each contributing project of aplurality of contributing projects within the plurality of projectsbeing associated with ordered auxiliary project information, the orderedauxiliary project information comprising a plurality of items maintainedto be accessed in order as sorted by a key, the local entitycorresponding to each contributing project being associated with theordered auxiliary project information also associated with thatcontributing project, wherein the processor-implemented engine isfurther directed to: a) dynamically aggregate the ordered auxiliaryproject information via a merging process across a contiguous pluralityof local projects selected by the user within the plurality of localentities and comprising the respective at least one source constituentlocus project for each project in the contiguous plurality of localprojects and the respective inherited entity corresponding to aninheritable contributing project of the at least one inheritable entityand of the plurality of contributing projects, generating adynamically-changing aggregation comprising an aggregated plurality ofitems within the plurality of items; and b) present thedynamically-changing aggregation to the user, thereby enabling the user,while exploring the plurality of local projects, being a customizedcollection of projects comprising the respective inherited entitycorresponding to the inheritable contributing project within theintegrated hierarchy, as ascended or descended in the localized DAG fromthe at least one constituent locus project, to visualize thedynamically-changing aggregation of the ordered auxiliary projectinformation across the contiguous plurality of local projects, theordered auxiliary project information associated with a now-excludedproject of the plurality of contributing projects being removed from thedynamically-changing aggregation upon removal of the local projectcorresponding to the now-excluded project from the contiguous pluralityof local projects, a first item of the aggregated plurality of itemsbeing of the ordered auxiliary project information associated with afirst inheritable contributing ancestor of the inheritable contributingproject through the respective proper refinement ancestor project forthe first inheritable contributing ancestor and a second item of theaggregated plurality of items being of the ordered auxiliary projectinformation associated with a second inheritable contributing ancestorof the inheritable contributing project through the respective properrefinement ancestor project for the second inheritable contributingancestor.
 24. The apparatus of claim 21, wherein: upon an in-placemodification by the user to an original inherited entity, the originalinherited entity being the respective inherited entity corresponding toa given inheritable entity of the at least one inheritable entity,yielding a modified inherited entity, the original inherited entitycorresponding to the given inheritable entity being descended in thelocalized DAG from the respective constituent inheriting locus projectfor the given inheritable entity by the respective inheritingassociation, the client relates the original inherited entity to therespective constituent inheriting locus project for the giveninheritable entity by requesting the server to create in the global DAG,yielding a resulting global DAG: a) a restating entity, wherein therestating entity is created as an entity in the plurality of entitiesand the modified inherited entity corresponds to the restating entity;b) a first association with the restating entity as the child entity andwith the respective inheriting locus project for the given inheritableentity as the parent entity, wherein the first association is created asan association in the plurality of associations; and c) a secondassociation with the restating entity as the child entity and with thegiven inheritable entity as the parent entity, wherein the secondassociation is created as a refinement association in the plurality ofrefinement associations, thereby enabling the user to relate theoriginal inherited entity corresponding to the given inheritable entityto the respective constituent inheriting locus project for the giveninheritable entity in-place, the server maintaining the in-placemodification in the restating entity and leaving the given inheritableentity unchanged.
 25. The apparatus of claim 24, wherein: a) theplurality of projects subsumes a plurality of problems and a pluralityof solutions, no project being in both the plurality of problems and theplurality of solutions; b) the plurality of refinement associationscomprises: i) a problem refinement association that relates a childproblem of the plurality of problems and a parent problem of theplurality of problems, indicating that the child problem specializes theparent problem; or ii) a solution refinement association that relates achild solution of the plurality of solutions and a parent solution ofthe plurality of solutions, indicating that the child solutionelaborates upon the parent solution; and c) the given inheritable entityis a given inheritable project of the plurality of projects and therestating entity is a restating project of the plurality of projects,wherein: i) the given inheritable project is a given inheritablesolution of the plurality of solutions, the respective inherited entitycorresponding to the given inheritable solution being a given inheritedsolution of the plurality of local entities, the respective inheritinglocus project for the given inheritable solution being a respectiveinheriting locus problem of the plurality of problems and the respectiveproper refinement ancestor project for the given inheritable solutionbeing a respective proper refinement ancestor problem of the pluralityof problems, and the restating project is a restating solution createdas a solution in the plurality of solutions; or ii) the giveninheritable project is a given inheritable problem of the plurality ofproblems, the respective inherited entity corresponding to the giveninheritable problem being a given inherited problem of the plurality oflocal entities, the respective inheriting locus project for the giveninheritable problem being a respective inheriting locus solution of theplurality of solutions and the respective proper refinement ancestorproject for the given inheritable problem being a respective properrefinement ancestor solution of the plurality of solutions, and therestating project is a restating problem created as a problem in theplurality of problems, thereby enabling the user to visualize asdescended in the localized DAG from the respective constituentinheriting locus project and to initiate the in-place modification uponthe given inherited solution corresponding to the given inheritablesolution, the given inheritable solution addressing the respectiveproper refinement ancestor problem, a more general problem than therespective inheriting locus problem, and the restating solutionaddressing the respective inheriting locus problem, the servermaintaining the in-place modification in the restating solution andleaving the given inheritable solution unchanged, or the given inheritedproblem corresponding to the given inheritable problem, the giveninheritable problem decomposing the respective proper refinementancestor solution, a less elaborate solution than the respectiveinheriting locus solution, and the restating problem decomposing therespective inheriting locus solution, the server maintaining thein-place modification in the restating problem and leaving the giveninheritable problem unchanged.
 26. The apparatus of claim 25, the atleast one locus project being at least one locus problem of theplurality of problems, the at least one locus problem being descended inthe global DAG from at least one data-based context problem of theplurality of problems, each data-based context problem of the at leastone data-based context problem being implicitly or explicitly associatedwith a respective database of a plurality of databases, the respectivedatabase for each data-based context problem comprising data arranged asa plurality of attributes, wherein: a) the plurality of entitiessubsumes a plurality of condition components subsuming a plurality ofterms that express equalities or inequalities over at least oneattribute for at least one database of the plurality of databases andcomprising at least one Boolean operator; b) the given inheritableentity is a given inheritable condition component of the plurality ofcondition components, the respective inherited entity corresponding tothe given inheritable condition component being an original inheritedcondition component of the plurality of local entities; c) the in-placemodification by the user comprises a condition specialization operationperformed upon a representation of the original inherited conditioncomponent corresponding to the given inheritable condition componentwithin a representation of a condition associated with the at least onelocus problem; and d) the restating entity is a restating conditioncomponent of the plurality of condition components, thereby enabling theuser to specialize the condition by applying the conditionspecialization operation in-place to the original inherited conditioncomponent corresponding to the given inheritable condition component,the server maintaining the in-place modification in the restatingcondition component and leaving the given inheritable conditioncomponent unchanged.
 27. The apparatus of claim 26, wherein: a) theplurality of condition components comprises a disjunct deletionoperator; b) the given inheritable condition component is a giveninheritable disjunct-to-be-deleted; c) the condition is a disjunctionand the in-place modification by the user comprises a deletionoperation; and d) the restating entity is the disjunct deletionoperator, thereby enabling the user to specialize a disjunctioncondition associated with the at least one locus problem by removing thegiven inheritable disjunct-to-be-deleted in-place from the disjunctioncondition.
 28. The apparatus of claim 25 wherein: a) the plurality ofentities subsumes a plurality of state machine components subsuming aplurality of state machine states; b) the given inheritable entity is agiven inheritable state machine component of the plurality of statemachine components, the respective inherited entity corresponding to thegiven inheritable state machine component being an original inheritedstate machine component of the plurality of local entities; c) thein-place modification by the user comprises a state machine elaborationoperation performed upon a representation of the original inheritedstate machine component corresponding to the given inheritable statemachine component within a representation of a state machine associatedwith the at least one locus project; and d) the restating entity is arestating state machine component of the plurality of state machinecomponents, thereby enabling the user to elaborate the state machine byapplying the state machine elaboration operation in-place to theoriginal inherited state machine component, the server maintaining thein-place modification in the restating entity to participate in alower-level state machine and leaving the given inheritable entityunchanged to participate in a higher-level state machine.
 29. Theapparatus of claim 21, wherein: for each selected inherited entity of atleast one selected inherited entity of the plurality of local entities,that selected inherited entity corresponding to a respective selectedinheritable entity, that selected inherited entity being descended inthe localized DAG from the respective constituent inheriting locusproject for the respective selected inheritable entity by an inheritedentity path, the inherited entity path being a sequence comprising atleast one original inherited path entity of the plurality of localentities, the client relates that selected inherited entity to therespective constituent inheriting locus project for the respectiveselected inheritable entity by, for each original inherited path entitynot already visited of the at least one original inherited path entity,that original inherited path entity being the respective inheritedentity corresponding to a respective given inheritable path entity ofthe at least one inheritable entity, prompting the user for an in-placemodification to restate that original inherited path entity to therespective constituent inheriting locus project for the respectiveselected inheritable entity, yielding a modified inherited path entity,and requesting the server to create in the global DAG, yielding aresulting global DAG: a) a restating entity that restates the respectivegiven inheritable path entity for that original inherited path entity,wherein the restating entity that restates the respective giveninheritable path entity is created as an entity in the plurality ofentities and the modified inherited path entity corresponds to therestating entity that restates the respective given inheritable pathentity; b) a first association with the restating entity that restatesthe respective given inheritable path entity as the child entity andeither with the respective inheriting locus project for the respectivegiven inheritable path entity as the parent entity, if the respectiveinheriting locus project for the respective given inheritable pathentity is the parent entity of the modified inherited path entity alongthe respective inherited entity path, or else with the restating entitythat restates the immediately subsequent entity as the parent entity,wherein the first association is created as an association in theplurality of associations; and c) a second association with therestating entity that restates the respective given inheritable pathentity as the child entity and with the respective given inheritablepath entity as the parent entity, wherein the second association iscreated as a refinement association in the plurality of refinementassociations, thereby enabling the user to relate each selectedinherited entity to the respective constituent inheriting locus projectfor the respective selected inheritable entity by modifying in-placeeach inherited path entity along each inherited entity path, the servermaintaining the in-place modification in each restating entity andleaving the respective given inheritable path entity for each originalinherited path entity unchanged.
 30. The apparatus of claim 21, wherein:for each selected inherited entity of at least one selected inheritedentity of the plurality of local entities, that selected inheritedentity corresponding to a respective selected inheritable entity, thatselected inherited entity being descended in the localized DAG from therespective constituent inheriting locus project for the respectiveselected inheritable entity by an inherited entity path, the inheritedentity path being a sequence comprising at least one original inheritedpath entity of the plurality of local entities, the client relates thatselected inherited entity to the respective constituent inheriting locusproject for the respective selected inheritable entity by, for eachoriginal inherited path entity not already visited of the at least oneoriginal inherited path entity and of one or more inherited entities tobe restated, the one or more inherited entities to be restatedcomprising at least one inherited entity from within any contiguoussequence of entities along the inherited entity path, any pair ofadjacent entities within that contiguous sequence being related byrefinement, at least one inherited path entity not to be restated beingof the at least one original inherited path entity and not being of theone or more inherited entities to be restated, that original inheritedpath entity being the respective inherited entity corresponding to arespective given inheritable path entity of the at least one inheritableentity, prompting the user for an in-place modification to restate thatoriginal inherited path entity to the respective constituent inheritinglocus project for the respective selected inheritable entity, yielding amodified inherited path entity, and requesting the server to create inthe global DAG, yielding a resulting global DAG: a) a restating entitythat restates the respective given inheritable path entity for thatoriginal inherited path entity, wherein the restating entity thatrestates the respective given inheritable path entity is created as anentity in the plurality of entities and the modified inherited pathentity corresponds to the restating entity that restates the respectivegiven inheritable path entity; b) a first association with the restatingentity that restates the respective given inheritable path entity as thechild entity and either with the respective inheriting locus project forthe respective selected inheritable entity as the parent entity, if nosubsequent original inherited path entity subsequent to that originalinherited path entity along the respective inherited entity path isamong the one or more inherited entities to be restated, or else withthe restating entity that restates a nearest subsequent inheritable pathentity as the parent entity, a nearest subsequent original inheritedpath entity towards the respective constituent inheriting locus projectfor the respective selected inheritable entity along the respectiveinherited entity path among the one or more inherited entities to berestated corresponding to the nearest subsequent inheritable pathentity, wherein the first association is created as an association inthe plurality of associations; and c) a second association with therestating entity that restates the respective given inheritable pathentity as the child entity and with the respective given inheritablepath entity as the parent entity, wherein the second association iscreated as a refinement association in the plurality of refinementassociations, thereby enabling the user to relate each selectedinherited entity to the respective constituent inheriting locus projectfor the respective selected inheritable entity by modifying in-place atleast one representative inherited path entity in each sequence ofrefinement associations along each inherited entity path, the servermaintaining the in-place modification in each restating entity andleaving the respective given inheritable path entity for each of the atleast one representative inherited path entity unchanged, avoidingcreation of entities and associations to restate the at least oneinherited path entity not to be restated.
 31. An apparatus comprising: aprocessor-implemented engine, memory coupled to theprocessor-implemented engine; and networking hardware supporting theprocessor-implemented engine in acting as a server communicating withone or more computing devices, wherein the processor-implemented engineis directed according to instructions stored in the memory to: a)receive identification of at least one locus entity of a plurality ofentities from a client; b) extract a respective localized directedacyclic graph (DAG) localized to the at lease one locus entity, therespective localized DAG of a plurality of localized DAGs, from a globalDAG comprising the plurality of entities and a plurality ofassociations, each association of the plurality of associations relatinga child entity and a parent entity of the plurality of entities, and; c)transfer the respective localized DAG to the client, the respectivelocalized DAG comprising: 1) a plurality of local entities comprising aconstituent entity corresponding to each entity of a plurality ofparticular reachable entities within the plurality of entities, eachentity of the plurality of particular reachable entities being ascendedor descended in the global DAG from a respective at least one sourcelocus entity of the at least one locus entity by a respective at leastone path, at least one constituent locus entity corresponding to the atleast one locus entity; and 2) a plurality of local associationscomprising a constituent association corresponding to each associationof the plurality of associations on the respective at least one path foreach entity of the plurality of particular reachable entities, thatconstituent association relating the constituent entity corresponding tothe child entity for that association as a child local entity and theconstituent entity corresponding to the parent entity for thatassociation as a parent local entity, wherein: i) the plurality ofentities subsumes a plurality of projects and the plurality ofassociations subsumes a plurality of refinement associations, eachrefinement association of the plurality of refinement associationsindicating that the child entity for that refinement association refinesthe parent entity for that refinement association; and ii) for aselected context project of the plurality of local entities andcorresponding to a selected project of the plurality of projects, theserver generalizes the respective at least one path for the selectedcontext project by, for each context collection in a sequence of contextcollections, the sequence of context collections comprising a firstcontext collection and a final context collection, that contextcollection comprising one or more context entities of the plurality oflocal entities, the one or more context entities not related to eachother as ancestors or descendants in the respective localized DAG, eachcontext entity of the one or more context entities of the first contextcollection corresponding to a respective locus entity of the at leastone locus entity, each parent context entity in the parent contextcollection being properly ascended in the global DAG from at least oneentity in that context collection, the parent context collectioncomprising a proper ancestor of each context entity in the contextcollection, creating in the global DAG, yielding a resulting global DAG:a. a generalizing entity that generalizes that context collection,wherein the generalizing entity is created as an entity in the pluralityof entities based on input provided by a user of the client; b. a firstassociation with the generalizing entity that generalizes that contextcollection as the child entity and either with the generalizing entitythat generalizes a parent context collection succeeding that contextcollection in the sequence of context collections, or, where thatcontext collection is the final context collection in the sequence ofcontext collections, with the selected context project as the parententity, wherein the first association is created as an association inthe plurality of associations; and c. for each context entity in thatcontext collection, a respective second association with that contextentity as the child entity and with the generalizing entity as theparent entity, wherein the respective second association is created as arefinement association in the plurality of refinement associations,thereby generalizing each context collection in the sequence of contextcollections, supporting the client in enabling the user to generalizethe respective at least one path for the selected context project. 32.The apparatus of claim 31, wherein the server receives identification ofat least one locus project of the plurality of projects from a secondclient and transfers to the second client the respective localized DAGfor the at least one locus project, the sequence of context collectionsbeing a single context collection, the respective at least one sourcelocus entity of the at least one locus entity for the selected projectbeing one source locus entity, a path of the respective at least onepath from the one source locus entity for the selected projectcomprising a refinement descendant project that is descended in theglobal DAG from the selected project by a refinement path by way of asequence of one or more refinement associations of the plurality ofrefinement associations, the at least one locus project comprising arefinement descendant locus project that is descended in the global DAGfrom the selected project by a second refinement path, the refinementdescendant locus project not being ascended or descended in the globalDAG from the refinement descendant project, wherein: theprocessor-implemented engine is further directed to perform areconfiguration upon the respective localized DAG for the at least onelocus project, the reconfiguration comprising, for each inheritableentity of a respective at least one inheritable entity of the pluralityof entities for the at least one locus project, that inheritable entitydescended in the global DAG from a respective inheritable child entityby a respective inheritable entity path, the plurality of projectscomprising a respective proper refinement ancestor project that isrelated as a parent in the global DAG to the respective inheritablechild entity and that is ascended in the global DAG from a respectiveinheriting locus project of the at least one locus project by arespective inheritance path by way of a respective sequence of one ormore refinement associations of the plurality of refinementassociations, a respective constituent inheriting locus project of theat least one constituent locus project corresponding to the respectiveinheriting locus project: A) where that inheritable entity is anon-locus-descended inheritable entity not descended in the global DAGfrom any locus project of the at least one locus project: I) theplurality of local entities of the respective localized DAG for the atleast one locus project comprising a respective inherited entitycorresponding to the non-locus-descended inheritable entity; and II) theplurality of local associations of the respective localized DAG for theat least one locus project comprising a respective inheritingassociation with the respective inherited entity corresponding to thenon-locus-descended inheritable entity as the child local entity andwith the respective constituent inheriting locus project for thatinheritable entity being ascended in the respective localized DAG forthe at least one locus project from the parent local entity; and B)where that inheritable entity is a locus-descended inheritablecomponent, an already-inherited-or-constituent component correspondingto the locus-descended inheritable component being descended in therespective localized DAG for the at least one locus project from therespective constituent inheriting locus project for that inheritableentity: I) the plurality of local associations of the respectivelocalized DAG for the at least one locus project comprising a respectivemerging association with the already-inherited-or-constituent componentas the child local entity and with a parent inherited entitycorresponding to the parent of the locus-descended inheritable componentalong the respective inheritable entity path as the parent local entity,wherein the one source locus entity is not among the respective at leastone inheritable entity for the at least one locus project therebysupporting the client in avoiding distracting the user navigating to theat least one locus project with the one source locus entity, restatingwith respect to the refinement descendant project, unrelated to therefinement descendant locus project.
 33. The apparatus of claim 31,wherein the server receives identification of at least one locus projectof the plurality of projects from a second client and transfers to thesecond client the respective localized DAG for the at least one locusproject, the sequence of context collections being a single contextcollection, the respective at least one source locus entity for theselected project being one source locus entity, a path of the respectiveat least one path for the selected project and the one source locusentity comprising a refinement descendant project that is descended inthe global DAG from the selected project by a refinement path by way ofa sequence of one or more refinement associations of the plurality ofrefinement associations, the at least one locus project comprising arefinement descendant locus project that is descended in the global DAGfrom the refinement descendant project, being related as a parent to theone source locus entity by an association, by a continued refinementpath by way of a continued sequence of one or more refinementassociations of the plurality of refinement associations wherein: theprocessor-implemented engine is further directed to perform areconfiguration upon the respective localized DAG for the at least onelocus project, the reconfiguration comprising, for each inheritableentity of a respective at least one inheritable entity of the pluralityof entities for the at least one locus project, that inheritable entitydescended in the global DAG from a respective inheritable child entityby a respective inheritable entity path, the plurality of projectscomprising a respective proper refinement ancestor project that isrelated as a parent in the global DAG to the respective inheritablechild entity and that is ascended in the global DAG from a respectiveinheriting locus project of the at least one locus project by arespective inheritance path by way of a respective sequence of one ormore refinement associations, a respective constituent inheriting locusproject of the at least one constituent locus project corresponding tothe respective inheriting locus project: A) where that inheritableentity is a non-locus-descended inheritable entity not descended in theglobal DAG from any locus project of the at least one locus project: I)the plurality of local entities of the respective localized DAG for theat least one locus project comprising a respective inherited entitycorresponding to the non-locus-descended inheritable entity; and II) theplurality of local associations of the respective localized DAG for theat least one locus project comprising a respective inheritingassociation with the respective inherited entity corresponding to thenon-locus-descended inheritable entity as the child local entity andwith the respective constituent inheriting locus project for thatinheritable entity being ascended in the respective localized DAG forthe at least one locus project from the parent local entity; and B)where that inheritable entity is a locus-descended inheritablecomponent, an already-inherited-or-constituent component correspondingto the locus-descended inheritable component being descended in therespective localized DAG for the at least one locus project from therespective constituent inheriting locus project for that inheritableentity: I) the plurality of local associations of the respectivelocalized DAG for the at least one locus project comprising a respectivemerging association with the already-inherited-or-constituent componentas the child local entity and with a parent inherited entitycorresponding to the parent of the locus-descended inheritable componentalong the respective inheritable entity path as the parent local entity,wherein the generalizing entity is not among the respective at least oneinheritable entity for the at least one locus project, therebysupporting the client in avoiding distracting the user navigating to theat least one locus project with the generalizing entity, related to theselected project by the first association, the one source locus entitybeing among the respective at least one inheritable entity for the atleast one locus project and refining the generalizing entity, the onesource locus entity related as a child to the refinement descendantproject by the association, the refinement descendant project descendedin the global DAG from the selected project by the refinement path.